Inference Data Cookbook

InferenceData is the central data format for ArviZ. InferenceData itself is just a container that maintains references to one or more xarray.Dataset. See the InferenceData structure specification here. Below are various ways to generate an InferenceData object. See here for more on xarray.

Table of contents

  1. From 1d numpy array
  2. From nd numpy array
  3. From a dictionary
  4. From dictionary with coords and dims
  5. From PyMC3
  6. From PyStan
  7. From Pyro
  8. From emcee
  9. From CmdStanPy
  10. From CmdStan
  11. From NumPyro
  12. From PyJAGS
[1]:
import arviz as az
import numpy as np

Bad key "text.kerning_factor" on line 4 in
/Users/michaelnowotny/anaconda3/envs/continuous_time_mcmc/lib/python3.7/site-packages/matplotlib/mpl-data/stylelib/_classic_test_patch.mplstyle.
You probably need to get an updated matplotlibrc file from
https://github.com/matplotlib/matplotlib/blob/v3.1.3/matplotlibrc.template
or from the matplotlib source distribution

From 1d numpy array

[2]:
size = 100
dataset = az.convert_to_inference_data(np.random.randn(size))
dataset
[2]:
arviz.InferenceData
    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 1
        • draw: 100
        • chain
          (chain)
          int64
          0
          array([0])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 6 ... 94 95 96 97 98 99
          array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
                 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
                 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
                 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,
                 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
                 90, 91, 92, 93, 94, 95, 96, 97, 98, 99])
        • x
          (chain, draw)
          float64
          0.03666 -0.5439 ... 0.06209 0.6484
          array([[ 0.03665646, -0.54393088,  0.25816287, -0.88667309, -0.9348225 ,
                   0.33301484, -0.84429579, -1.4424599 , -0.10404786, -1.29350824,
                  -0.39855624,  0.73392032, -1.04056388,  0.90595297, -0.33542889,
                   0.71002635, -0.93332042,  0.90383559,  0.55048459,  0.84419701,
                   0.31012583, -0.84100256, -0.39144559, -1.13356245,  0.85805521,
                  -1.23666159, -0.83417515,  2.00148204,  0.18593225, -0.57290472,
                  -0.84720181, -1.03068615,  0.26563499, -0.07248018,  0.49226217,
                  -0.83664213, -0.06930488, -0.42508101, -0.50932109, -2.03953584,
                  -0.50155511,  0.84223862,  0.98786079,  1.95306512, -0.00238945,
                   0.84154059,  1.09332188,  0.09321012, -1.32853295,  0.86016117,
                   0.03143054, -0.73582048,  0.60286073, -0.27524679,  0.06912192,
                  -0.02616594,  0.13402047, -0.28841993, -0.28717231,  0.49984188,
                  -1.42709621, -1.08839178,  1.42256533, -2.04966982,  0.1603367 ,
                   0.74942004, -0.79721512, -0.39401085, -0.63873233, -1.35973308,
                  -1.43679545,  0.25916161, -0.19478977,  0.13274431, -0.69982524,
                   0.98709261, -0.21108074, -0.58446043,  1.04648878,  0.29844901,
                  -0.799379  , -0.97175979, -1.89425023,  0.4809745 ,  0.61937049,
                   1.31717397,  0.78575551,  0.76162552, -0.49251748, -1.21425305,
                  -2.14832528,  0.06044719, -1.34104858, -0.08645523,  0.56492468,
                   1.9975031 , -1.13772208,  0.23265261,  0.06208744,  0.6484334 ]])
      • created_at :
        2020-06-10T18:19:03.719498
        arviz_version :
        0.8.3

From nd numpy array

[3]:
shape = (1, 2, 3, 4, 5)
dataset = az.convert_to_inference_data(np.random.randn(*shape))
dataset
[3]:
arviz.InferenceData
    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 1
        • draw: 2
        • x_dim_0: 3
        • x_dim_1: 4
        • x_dim_2: 5
        • chain
          (chain)
          int64
          0
          array([0])
        • draw
          (draw)
          int64
          0 1
          array([0, 1])
        • x_dim_0
          (x_dim_0)
          int64
          0 1 2
          array([0, 1, 2])
        • x_dim_1
          (x_dim_1)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • x_dim_2
          (x_dim_2)
          int64
          0 1 2 3 4
          array([0, 1, 2, 3, 4])
        • x
          (chain, draw, x_dim_0, x_dim_1, x_dim_2)
          float64
          -0.921 0.4821 ... -1.388 -0.2951
          array([[[[[-0.92101852,  0.48214847, -1.34675845,  0.80791591,
                      0.13442397],
                    [ 1.55928147,  0.72467009, -0.26329447,  0.77020337,
                     -0.79385986],
                    [ 2.56014158, -0.22522851,  1.50429511,  0.98422616,
                      0.87701818],
                    [ 0.2033265 , -0.46213057,  1.83291516,  0.92185653,
                      0.02246557]],
          
                   [[ 0.58975218,  0.2109381 , -0.25165215,  1.07386412,
                      0.22433061],
                    [-0.38069638,  0.17451069, -0.91240345, -1.14499426,
                      0.2878055 ],
                    [-1.75288879,  0.81279251, -0.92868769,  0.805726  ,
                     -0.79796633],
                    [-0.73333509, -0.1039633 , -1.59234066, -0.72387975,
                      0.73062838]],
          
                   [[ 0.71570935,  0.52509819, -0.36251886, -1.60016203,
                     -0.23893154],
                    [-0.06835913, -1.21852009,  0.82192727, -1.10977168,
                     -2.08662438],
                    [-0.20764243, -0.14951083, -0.60938158,  1.3045079 ,
                      1.49413921],
                    [-0.77821166, -0.88093741,  0.3519268 ,  0.20628867,
                     -1.56463733]]],
          
          
                  [[[ 0.70988028, -0.71212251,  0.25541438,  0.05158433,
                      0.75728211],
                    [-0.10089313, -2.0769755 , -3.32968542,  0.88509685,
                      0.53247162],
                    [ 0.73857681, -1.82011301,  0.86925206,  0.70125327,
                     -0.35396124],
                    [-0.49242067,  0.25316   ,  0.18691584,  0.63272798,
                     -0.87052449]],
          
                   [[ 0.16249541, -0.76002895, -0.57382345,  0.31514025,
                      0.05763214],
                    [-0.73349012,  0.373515  , -1.79050181,  0.14774867,
                     -0.65746071],
                    [ 1.55594162, -0.14762212, -2.85498527,  1.43403387,
                     -0.74873244],
                    [ 1.0050118 ,  0.44536177, -0.15660396,  0.65484298,
                     -0.84545377]],
          
                   [[ 1.78973096, -0.3529071 , -0.73334952,  0.64730247,
                      0.21085732],
                    [-0.87333169,  1.23147537, -0.09859236,  1.002286  ,
                     -1.4012664 ],
                    [-0.85472506, -0.24004629, -0.04136821, -0.90713131,
                      0.22470241],
                    [-0.2516493 ,  1.97247898, -0.16846266, -1.38770486,
                     -0.29507746]]]]])
      • created_at :
        2020-06-10T18:19:03.796075
        arviz_version :
        0.8.3

From a dictionary

[4]:
datadict = {
    "a": np.random.randn(100),
    "b": np.random.randn(1, 100, 10),
    "c": np.random.randn(1, 100, 3, 4),
}
dataset = az.convert_to_inference_data(datadict)
dataset
[4]:
arviz.InferenceData
    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • b_dim_0: 10
        • c_dim_0: 3
        • c_dim_1: 4
        • chain: 1
        • draw: 100
        • chain
          (chain)
          int64
          0
          array([0])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 6 ... 94 95 96 97 98 99
          array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
                 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
                 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
                 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,
                 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
                 90, 91, 92, 93, 94, 95, 96, 97, 98, 99])
        • b_dim_0
          (b_dim_0)
          int64
          0 1 2 3 4 5 6 7 8 9
          array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
        • c_dim_0
          (c_dim_0)
          int64
          0 1 2
          array([0, 1, 2])
        • c_dim_1
          (c_dim_1)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • a
          (chain, draw)
          float64
          -0.9868 -0.9059 ... -0.08585 0.2419
          array([[-0.98680087, -0.9059364 , -0.14165402, -0.58265096,  0.82603876,
                  -2.46304762, -0.68751032, -0.44797211,  0.4767166 ,  1.20762507,
                   1.7683901 ,  0.49919964,  0.39169713,  0.24818252,  0.76896913,
                   1.35602941,  0.16012735, -0.40869246,  1.57454222, -0.88422323,
                  -0.8032874 ,  0.97983047,  0.62862413,  0.86092572,  1.28611767,
                   0.47059445, -1.94828812,  0.77238202,  1.34715668,  0.5508723 ,
                   0.37690772,  0.36441709,  1.00628099, -0.25510614, -0.15580706,
                  -2.12785677,  1.51691814, -1.11203406,  0.15787474,  0.49807416,
                   0.59557061,  1.31281552,  0.81375214, -0.23155098,  0.33571588,
                  -0.57863365, -0.28264525, -0.09610144, -0.54420598, -0.6172331 ,
                  -0.7610177 , -0.46448357, -0.35348013,  0.14209789, -1.24727987,
                   0.01894142,  1.5554319 , -1.58654114, -1.04792336,  1.60558452,
                  -1.55497944,  0.42248955, -0.01063844,  0.37625908,  0.32187246,
                  -0.90741871,  0.70642742,  1.4723044 , -1.05279937,  0.48145175,
                  -0.70126199, -0.93931202, -0.48064917,  0.0822739 , -1.60523997,
                   1.33511812,  0.80697787, -0.43798262, -1.12562896,  0.99484913,
                  -1.57580105,  1.12748292, -1.16916992,  0.26178148,  0.10459207,
                   1.53168163,  0.43148325, -0.05799433,  0.48346788,  0.34411697,
                   0.00835765, -0.99452364, -2.11526315,  1.13121207, -0.30909674,
                   0.43876463, -0.3636197 , -0.3043917 , -0.08585393,  0.2418645 ]])
        • b
          (chain, draw, b_dim_0)
          float64
          -0.6033 0.6579 ... 0.09994 -0.8692
          array([[[-6.03344744e-01,  6.57856984e-01,  3.44548919e-01,
                    3.00142169e-01, -5.26833619e-01,  3.29689332e-01,
                   -1.31465481e-01, -1.11881896e+00,  1.18846301e+00,
                   -1.21813909e+00],
                  [ 1.17352705e+00,  4.49529097e-01, -7.83719405e-01,
                    7.05153489e-01,  7.20493088e-01, -1.65224704e-01,
                    9.02912425e-01,  8.19731087e-01, -3.36621748e-01,
                   -5.87045111e-01],
                  [-9.96082427e-01,  4.77531075e-01, -2.34510302e+00,
                    1.68160162e+00,  6.22797427e-03,  1.77374788e+00,
                   -1.50265600e+00,  3.11192598e-01,  1.91409288e-01,
                    7.48532726e-01],
                  [-2.18461121e+00,  1.50224313e+00, -8.48418441e-02,
                    1.56111055e-01, -6.28023349e-01,  2.44065494e+00,
                    1.34358128e+00,  6.45792256e-02, -5.37334375e-01,
                   -1.58412656e+00],
                  [-1.33605723e+00,  1.53919334e+00,  9.89398732e-01,
                    7.74029783e-02, -2.20688937e+00,  1.18267626e-01,
                   -5.69714810e-03, -1.15067825e+00,  5.68043096e-01,
                    7.70411480e-01],
                  [-1.13852033e+00,  3.47448503e-01,  1.52309065e+00,
                   -1.32490172e+00, -2.32465532e-01,  8.68848166e-01,
                   -6.16837275e-02,  1.33329233e+00,  7.29225621e-02,
                    7.24641776e-01],
                  [-1.15838246e+00, -8.26426337e-01, -4.57894659e-01,
                    4.56794856e-01,  3.10055489e-01, -1.79734037e-02,
                   -9.84080320e-01, -1.29296979e+00, -8.40349545e-02,
                    2.58786373e-01],
                  [ 5.51656105e-01,  1.43825410e+00, -4.36959135e-01,
                   -5.78931413e-02,  1.29019244e+00,  4.36264408e-01,
                    1.33306016e+00,  2.58902126e+00,  2.18743344e+00,
                   -4.36414636e-01],
                  [-1.15194329e+00,  5.74085856e-01, -6.80884765e-01,
                    1.38353054e+00, -2.72955555e-01, -1.32859425e+00,
                    2.24159658e+00, -1.85937277e+00, -6.25979461e-01,
                    2.98351415e-01],
                  [ 7.03720099e-01,  1.44173056e+00, -6.92558561e-02,
                    2.95877859e-01, -2.98021556e-01, -7.70862124e-01,
                   -1.08625934e+00,  1.04516406e+00, -1.85273444e+00,
                    2.06092575e+00],
                  [ 1.04401520e-01,  7.39694607e-01, -1.15940584e+00,
                   -5.81278186e-01, -1.38478532e+00,  1.83985938e+00,
                    1.85276646e+00,  1.14389132e+00, -8.46548159e-01,
                   -8.97060931e-01],
                  [-7.03963313e-01, -2.14852744e+00, -4.67196755e-01,
                   -1.28214529e+00,  1.56616160e+00, -2.29603438e+00,
                   -8.71054829e-01, -1.57125278e+00, -1.27717725e-01,
                    3.90472950e-01],
                  [ 9.32857554e-01, -1.62350199e+00, -1.18949692e-01,
                   -2.04093561e+00,  2.89166449e-01,  5.04334491e-01,
                   -8.08487490e-01, -6.45941332e-01, -3.10636191e-03,
                   -1.76777806e-02],
                  [ 3.28726794e-04,  7.64485340e-01,  1.17277547e+00,
                   -1.52697903e+00, -5.09176289e-01, -4.82164179e-01,
                   -2.26069420e-01, -6.12613334e-01, -6.19346794e-01,
                   -1.29346515e+00],
                  [-2.05227275e+00, -3.65561981e-02,  4.18985471e-01,
                    1.48795235e-01,  1.29697774e-01, -3.10792226e-01,
                   -2.66639794e-01, -8.91297615e-01, -5.62512864e-01,
                   -1.09868049e+00],
                  [ 4.23890956e-01, -9.35524984e-01, -4.25062985e-01,
                    3.30534938e-01,  1.36676232e+00,  1.00625155e+00,
                   -1.51675944e-02, -1.90166945e+00,  9.34924334e-01,
                   -1.22422149e+00],
                  [ 1.27950941e-01,  9.86967420e-01,  3.69754064e-01,
                   -1.06276533e+00, -4.18378711e-01, -7.63597916e-01,
                    1.90183960e-01,  9.90085182e-02,  1.08525123e+00,
                    2.17597127e-01],
                  [-9.63262514e-01,  7.81149102e-02, -3.20795189e-01,
                    4.05531512e-01, -7.26173288e-01, -1.01466534e+00,
                    2.03474395e+00, -1.24271091e-01,  1.93436249e+00,
                   -1.17909975e+00],
                  [-5.70649376e-01, -8.34619821e-01,  8.45542524e-01,
                   -7.42262280e-01,  1.14077178e-01,  4.97437579e-01,
                    2.20796720e+00, -1.42905324e-01, -8.24939696e-01,
                    1.40557906e+00],
                  [-6.95666653e-01, -1.74886824e-01,  1.71599123e+00,
                    5.86052743e-01, -2.16556634e-02, -4.10865757e-01,
                    1.49435198e+00, -8.70780433e-01,  2.85899854e-01,
                    8.68184593e-01],
                  [ 2.73823061e-01, -4.98582368e-01,  1.53582947e+00,
                   -9.14754419e-01,  9.71505598e-01,  9.92993972e-01,
                    5.96438243e-01, -2.86586036e-01,  1.95743478e+00,
                   -2.20829155e-01],
                  [ 1.63850220e+00,  2.95440786e-01,  1.30065186e+00,
                   -9.93511299e-02, -3.76079329e-01, -8.25564643e-01,
                   -1.61999376e-01, -1.14248430e-01,  1.27566333e+00,
                   -3.48046368e-01],
                  [-1.45762416e-01,  1.39621941e+00,  1.92237888e+00,
                    5.89155632e-01,  1.46429119e+00,  1.53810630e-01,
                    1.58447573e-01, -2.43321209e-01, -7.38333316e-01,
                   -1.23821968e+00],
                  [ 9.76117826e-01,  3.29990313e-01,  1.15123880e-01,
                    4.99346096e-01, -1.40186745e+00, -2.01628854e+00,
                    7.64935235e-01, -1.44727437e+00,  1.75402206e-01,
                   -7.43535801e-01],
                  [-1.19678596e+00,  8.15575342e-01,  3.45959027e-01,
                   -1.55267128e-01,  1.00092325e+00,  1.07173246e+00,
                   -8.76878757e-01, -1.65442667e+00, -1.94738497e+00,
                   -7.25719719e-01],
                  [-7.31290552e-03,  4.25956663e-01,  1.41045243e-02,
                   -9.38274013e-01, -1.44788155e+00, -3.44116787e-01,
                   -1.48523306e-01, -1.44559454e+00, -2.18867427e-01,
                    3.28646495e-01],
                  [ 5.42897524e-01,  1.94972122e-01, -2.91695697e-01,
                    7.66816314e-02,  7.58577867e-01,  1.63945182e-01,
                    3.83678569e-01, -1.74527148e-02,  9.51222174e-01,
                   -1.15197652e-03],
                  [-8.08403556e-01, -1.80543885e+00, -5.38675846e-02,
                   -1.09748280e+00, -3.38943085e-01, -8.89970856e-01,
                   -2.03799415e+00,  1.01699459e+00, -1.48642805e+00,
                   -4.51014926e-01],
                  [ 7.51352276e-01,  2.22660335e-01, -1.42399694e-01,
                    4.49104552e-01,  1.03711348e+00, -1.54627325e-01,
                   -9.89487696e-01, -1.11269767e+00,  9.21655993e-01,
                   -3.53273843e-01],
                  [-2.29251295e+00,  5.44184518e-02,  6.62783314e-01,
                   -7.95233752e-02, -4.51309564e-01,  3.92000090e-02,
                   -5.78584216e-01,  5.49292384e-01,  1.79005634e+00,
                   -2.44758103e-02],
                  [ 8.03690663e-01, -1.02272529e+00, -1.11828509e-01,
                    1.18464169e+00, -2.15790068e-01,  8.70460501e-01,
                   -1.27119386e+00,  9.25915153e-01,  1.33622293e+00,
                   -2.51928764e-01],
                  [-8.90111272e-01, -7.93194826e-01,  6.48713202e-02,
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                   -1.26484259e+00, -1.62428317e+00, -2.47432140e+00,
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                  [ 1.45782588e+00,  1.22470928e+00,  1.37059960e+00,
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                   -1.05703323e+00,  1.23446732e+00,  5.72544579e-01,
                    1.16824142e+00],
                  [ 7.91618805e-01, -1.51390117e+00, -9.58717632e-01,
                   -1.33186174e+00,  2.44159781e-01,  1.42667075e+00,
                   -1.93043316e-01,  1.13969662e+00,  1.14080836e+00,
                   -7.47563604e-01],
                  [-1.25234755e+00, -4.89458697e-01, -1.05419689e+00,
                   -3.61371620e-01, -1.35641263e-01,  9.26537840e-01,
                    1.94874715e+00,  3.53143290e-01, -1.00025902e+00,
                   -8.37607504e-01],
                  [ 9.43426257e-01, -1.41564714e+00,  1.45535179e-01,
                   -2.46613292e+00, -9.92801870e-01,  1.77217495e+00,
                   -6.32787481e-01,  3.53400806e-01,  5.75950370e-02,
                   -5.78596946e-01],
                  [-6.32177724e-01,  1.04906198e+00,  1.15932725e+00,
                   -6.95320997e-01, -2.09687542e+00,  1.13367200e+00,
                   -1.07877931e-03, -9.22808422e-02, -6.24162045e-01,
                   -4.88116120e-01],
                  [-2.89103638e-01,  1.46969037e+00,  1.50983980e+00,
                   -2.35424926e-01,  7.09090381e-02,  4.89436311e-01,
                    1.37263363e+00,  1.46094496e-01, -7.05583452e-01,
                    3.06267245e-01],
                  [ 1.11293488e+00, -1.25152498e+00,  1.74525215e-01,
                    4.06811364e-01, -1.83488761e-03,  1.81938683e-01,
                    1.29059447e+00,  1.17073440e+00,  9.99376107e-02,
                   -8.69229686e-01]]])
        • c
          (chain, draw, c_dim_0, c_dim_1)
          float64
          -0.1873 0.08068 ... -0.7178 -0.4593
          array([[[[-0.18733941,  0.08068124, -0.74981289,  1.14908319],
                   [-0.23887625,  0.77923397, -1.09384671,  0.85300368],
                   [ 0.11497364, -0.79956367, -0.65401389, -0.6553763 ]],
          
                  [[-0.0640023 , -0.3453749 , -0.21576098,  0.98122925],
                   [-0.39585305,  0.49347018,  0.63004415,  0.85404986],
                   [ 1.18751139, -0.85181631,  0.11780613,  0.80907842]],
          
                  [[ 1.65335708,  0.53322719,  0.30460134, -0.41337594],
                   [ 1.76889868,  0.8506907 ,  1.42290637,  1.08454681],
                   [ 1.37409373, -0.99599541, -0.12550746,  0.9409458 ]],
          
                  ...,
          
                  [[ 2.03811654,  0.96546731, -0.39226401,  0.74229003],
                   [ 0.19321198, -1.24549524, -1.60397554, -0.34112993],
                   [ 0.96758733, -1.13541144,  0.7103624 , -0.39037624]],
          
                  [[-2.70188938,  0.75490061, -0.14130135,  1.14492753],
                   [-0.4482847 ,  0.69491268, -0.14514184, -0.74449329],
                   [-0.71947702,  0.04130831,  0.67365237, -0.64708764]],
          
                  [[ 0.99678923,  0.74509977, -1.61810631,  1.25375022],
                   [ 1.23621678, -0.53127017,  0.16684273,  0.56542842],
                   [-1.31944647,  1.35283207, -0.71780795, -0.45929745]]]])
      • created_at :
        2020-06-10T18:19:03.842568
        arviz_version :
        0.8.3

From dictionary with coords and dims

[5]:
datadict = {
    "a": np.random.randn(100),
    "b": np.random.randn(1, 100, 10),
    "c": np.random.randn(1, 100, 3, 4),
}
coords = {"c1": np.arange(3), "c2": np.arange(4), "b1": np.arange(10)}
dims = {"b": ["b1"], "c": ["c1", "c2"]}

dataset = az.convert_to_inference_data(datadict, coords=coords, dims=dims)
dataset
[5]:
arviz.InferenceData
    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • b1: 10
        • c1: 3
        • c2: 4
        • chain: 1
        • draw: 100
        • chain
          (chain)
          int64
          0
          array([0])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 6 ... 94 95 96 97 98 99
          array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
                 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
                 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
                 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,
                 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,
                 90, 91, 92, 93, 94, 95, 96, 97, 98, 99])
        • b1
          (b1)
          int64
          0 1 2 3 4 5 6 7 8 9
          array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
        • c1
          (c1)
          int64
          0 1 2
          array([0, 1, 2])
        • c2
          (c2)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • a
          (chain, draw)
          float64
          0.05449 -0.7435 ... 1.77 -0.06081
          array([[ 0.05449388, -0.743533  , -0.32473799, -0.76209616, -0.15318108,
                  -0.05848062,  0.97717731, -0.48588421, -0.8726501 , -0.07552945,
                   0.83003715, -1.19688506, -1.1247065 , -0.6013013 , -0.49520942,
                  -1.84118918, -2.59702905, -1.30659788,  0.98327226,  0.27655716,
                  -1.82151708, -0.63585987, -0.2902761 , -1.12612464, -2.07791993,
                  -0.13276421,  0.62298463, -0.48540343, -0.00994651, -0.11829631,
                   1.01228631, -1.46444786, -0.78597604,  0.51325285,  0.13163611,
                   1.09484645,  1.68969085, -0.52343559,  1.026338  ,  1.43407182,
                  -0.7722721 , -0.57958438,  0.20528191,  0.61321184,  1.68564395,
                  -0.30374717,  0.71144957, -0.65677733,  0.84996284, -1.30093387,
                  -1.70843071,  0.74581651,  0.86280279,  2.27569422, -2.35786222,
                  -0.86084899,  1.21739243,  1.5936106 ,  1.09724853, -0.26861585,
                   2.61918066, -1.05169746, -1.0950662 ,  0.86920039, -0.45478166,
                  -1.16591212,  0.72980447, -1.74191861, -2.17641695,  0.41770966,
                   0.35722643,  0.30221771, -0.44295916, -0.2569641 ,  0.87502338,
                  -0.61832058, -0.48042925, -0.6697292 , -0.42490819, -0.6803645 ,
                   0.93372907, -0.94644329, -0.66789602, -0.60290496, -1.2474643 ,
                  -0.38570061,  2.14155655,  1.42725836, -0.17612467, -0.34821489,
                  -0.44672739, -1.71950312,  0.00706469,  0.45771954,  1.98270075,
                  -0.19073369,  0.89296637,  1.2797043 ,  1.76970708, -0.0608144 ]])
        • b
          (chain, draw, b1)
          float64
          0.3839 -0.4249 ... -0.1143 0.9299
          array([[[ 3.83949782e-01, -4.24922581e-01, -7.52450072e-01,
                    1.21234248e+00, -9.22548373e-01,  1.68237742e-01,
                    1.99966773e+00, -3.26202020e-01,  6.07073687e-01,
                    1.02603162e+00],
                  [ 5.99675466e-02, -6.68527204e-02,  1.53698961e+00,
                    7.30218204e-01,  9.35546946e-01,  3.33506001e-01,
                   -2.87332730e+00, -9.29787572e-01, -1.17752033e+00,
                    1.06869258e+00],
                  [-4.07316192e-01,  5.26275934e-01,  1.43789696e+00,
                    3.38223434e-01,  8.74268720e-01, -1.12870206e+00,
                   -1.58333161e-01,  2.40482598e-01,  6.66687355e-01,
                   -1.51603941e+00],
                  [-1.06800357e+00,  2.41715171e+00,  1.04449716e-01,
                   -2.25170807e+00, -1.05611451e-01, -2.02149474e+00,
                   -1.45532700e+00, -3.88297474e-01, -1.97361060e+00,
                   -1.56830162e+00],
                  [ 1.76291146e+00, -1.21929963e+00,  5.54212069e-01,
                    2.22470001e-01, -8.45363510e-01, -1.96532800e+00,
                   -1.69154874e+00, -3.15075022e-01, -6.70247876e-01,
                   -1.96827011e+00],
                  [-1.10074526e+00, -3.28861345e-02, -1.54599206e-01,
                   -5.87159767e-01, -5.68027773e-01, -3.39073687e+00,
                    8.23872261e-01, -1.74575654e+00,  2.07647066e+00,
                    5.67036800e-01],
                  [ 4.56109764e-01, -7.52974728e-02,  3.68002622e-01,
                    4.22306025e-01,  1.42035086e-01, -4.71555345e-01,
                   -1.40617288e-02,  2.13677626e-02, -1.24304685e+00,
                    6.89790239e-01],
                  [ 8.52533818e-01,  6.23537996e-01, -5.15118924e-01,
                   -5.29511347e-01,  1.12812095e+00,  1.57289578e+00,
                    1.10968372e+00,  1.65095343e-01,  1.64284234e-01,
                   -4.92346994e-02],
                  [-1.10327112e+00, -1.30902913e+00,  2.53922155e+00,
                   -1.03140054e+00,  2.86071931e-01, -1.09701784e+00,
                   -3.69774002e-01,  1.41517836e+00, -1.72944423e-01,
                   -2.12026122e-01],
                  [-1.50219780e+00, -2.91957306e-02, -7.52128963e-01,
                    1.58525273e+00, -4.15595218e-01,  1.02651538e+00,
                   -7.11375007e-01, -2.09104023e+00,  3.18268460e-01,
                   -5.82647576e-01],
                  [ 3.73359615e-01, -1.03221499e+00, -1.42464375e+00,
                    8.21063294e-01, -1.30223298e+00,  6.04896419e-01,
                    1.72032411e+00,  1.95756800e+00, -1.47355600e+00,
                   -1.08295782e+00],
                  [-2.09053829e-01, -9.20789263e-01,  6.90538387e-01,
                   -2.24909099e-01,  4.80351972e-01,  2.24447864e-01,
                    2.04021679e+00,  2.36314287e-01,  9.31508635e-01,
                    1.70587886e+00],
                  [ 8.23512231e-01, -4.11601643e-01,  7.40975886e-01,
                    5.34362638e-01, -8.41619744e-01,  3.10125279e-01,
                   -1.42290698e+00,  3.10667627e-01,  3.93114301e-01,
                   -7.12339482e-01],
                  [ 1.08797616e+00,  7.20099070e-01, -4.29989221e-01,
                   -1.00040414e+00,  5.23271947e-01, -1.26459219e+00,
                    5.76655277e-01, -1.50134399e-01,  2.27101382e-01,
                    3.22129696e-01],
                  [-5.54169108e-01,  8.76852061e-01, -1.49156442e+00,
                    1.31718085e+00, -6.62791250e-01,  1.88165336e+00,
                   -5.98252681e-01,  1.40909948e+00, -7.98402584e-01,
                    4.21543289e-01],
                  [-1.04607570e+00,  4.30123259e-01, -2.69978635e-02,
                   -5.42491021e-01, -7.92985426e-03, -8.34306048e-01,
                   -3.18437357e-01,  3.91265333e+00, -9.36230817e-02,
                    1.37540300e+00],
                  [ 3.74529640e-01,  1.28236224e+00, -8.52009056e-01,
                    8.68775144e-01, -7.57826344e-01,  1.15150197e+00,
                   -8.90333915e-01, -2.24407457e-01,  2.11361661e-01,
                    1.43793929e+00],
                  [ 7.54543106e-01, -1.85232222e-01, -5.83625517e-01,
                    7.43067821e-01,  1.29570911e+00, -1.55280742e-01,
                    2.22127015e-01,  1.52300482e-01, -1.96691075e-01,
                   -6.90925328e-01],
                  [ 1.55943492e+00,  9.79636059e-02,  9.24298490e-01,
                   -2.38505258e-01,  1.49451569e-01,  5.16898436e-01,
                    7.25136633e-01,  4.06703017e-01, -1.16765186e+00,
                    1.79479576e-01],
                  [ 1.13826388e+00, -2.11730429e+00,  3.91150465e-01,
                    1.00826341e+00, -1.67066715e+00, -6.92940666e-01,
                    3.95891782e-01,  4.87964854e-01,  4.76176214e-01,
                   -1.05981270e+00],
                  [ 1.27354503e+00,  1.50298815e+00,  3.06781617e+00,
                    5.41638316e-01, -6.38883941e-03, -2.10172402e+00,
                   -3.40211461e-01,  1.32993622e+00,  3.64584065e-02,
                    8.93081220e-01],
                  [ 1.28027306e+00,  2.87912392e-01,  1.85406734e+00,
                   -1.31126694e+00, -1.77439477e+00,  1.17038342e+00,
                   -1.55335582e+00, -9.70662966e-01, -4.14694856e-01,
                    6.56108555e-01],
                  [ 6.70757537e-01,  8.67990577e-01,  1.48922300e+00,
                    2.17002319e+00,  2.14355502e-01,  4.04583299e-01,
                   -1.87168157e-01,  4.54775098e-01,  1.34697528e-01,
                   -8.34087427e-01],
                  [ 4.24119098e-01,  5.66633209e-01, -1.19861504e+00,
                   -1.31563848e+00, -7.25982516e-01, -5.17331148e-01,
                    8.84768951e-01, -4.85917354e-01, -8.54276881e-01,
                    1.36941018e+00],
                  [-3.09892947e-01, -1.58699551e+00,  3.97868866e-02,
                   -3.10165049e+00, -2.80230898e+00, -1.15420832e+00,
                    8.88099145e-01,  1.36779300e+00,  3.44006608e-01,
                   -1.18284855e+00],
                  [-1.82115896e-01,  1.06281752e+00,  1.32763594e+00,
                    1.59602688e-01, -6.91284373e-01,  9.10461880e-01,
                    5.80002501e-01,  1.87414781e-02, -4.03623704e-01,
                   -3.82102626e-01],
                  [-6.81799324e-01,  1.18184847e-01,  1.40921857e+00,
                    1.00418841e+00, -4.57577497e-01, -1.83608257e+00,
                   -1.26165605e+00,  3.56089974e-01,  1.67843918e-01,
                   -1.67021245e+00],
                  [ 1.33015619e-01,  9.84767347e-01, -1.34370562e+00,
                    1.93797366e-01, -2.43972270e+00,  1.62700700e-01,
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                    1.30543149e+00],
                  [-8.13336282e-01,  1.54521584e-01, -1.09511375e+00,
                   -2.12038209e-01, -7.82434608e-02,  1.30723436e+00,
                    1.22188215e+00, -7.74347698e-01,  6.04237773e-01,
                    7.73778177e-01],
                  [-1.87547241e+00, -6.20104423e-01, -2.02975443e+00,
                    1.10876675e+00,  1.62313379e+00,  5.87526478e-01,
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                   -9.50972634e-01],
                  [-7.48596229e-01,  5.45682903e-02,  6.83283243e-01,
                   -1.25068701e+00,  2.61429783e-01, -5.63525533e-01,
                   -2.86841656e-01,  6.74705159e-01, -2.66028874e-01,
                    7.91013554e-01],
                  [-1.41285655e-02, -4.63138085e-02,  8.49283612e-02,
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                   -4.45885895e-01],
                  [-2.55280955e-02,  1.38700190e+00, -7.81854196e-01,
                    4.26796445e-01, -1.26503295e+00, -1.10968326e+00,
                    1.44455830e-01, -1.11230680e-01,  1.65363098e+00,
                    5.35557632e-01],
                  [-2.14733890e-01,  6.06964487e-01,  1.44978105e+00,
                   -9.45837341e-01, -4.29973797e-01, -1.08852215e+00,
                   -7.05789057e-01,  7.11343161e-01, -1.37566908e+00,
                    7.87936567e-01],
                  [ 6.97087963e-01,  1.96501901e+00,  6.12251827e-01,
                    1.02943753e+00,  9.88382431e-02,  6.87929442e-01,
                   -1.69308494e+00,  2.50033002e+00, -1.36783109e+00,
                   -1.30297673e+00],
                  [ 9.01490986e-03, -1.89158609e+00,  8.20792024e-01,
                    1.31587679e+00,  1.06936305e+00, -1.39920777e+00,
                    7.32514979e-01,  7.72266312e-02, -7.10758800e-01,
                   -1.06380058e+00],
                  [-4.42321448e-01,  2.88094591e-01, -1.53150556e+00,
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                    1.30429443e+00,  9.90883201e-01,  9.69138754e-01,
                    4.29088822e-01],
                  [ 1.86105972e-01, -1.29915140e+00,  2.69199028e-01,
                    1.20938217e-01, -7.69945277e-01,  1.52504958e+00,
                    9.45252230e-01, -2.89977352e-01,  6.28081893e-01,
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                  [ 5.12803448e-01,  2.57369759e-01, -4.30234402e-01,
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                  [ 3.90257776e-01,  9.08049180e-01,  3.22342252e-01,
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                    1.09658102e+00],
                  [-8.62976202e-01, -3.11828896e-01, -5.03721872e-01,
                   -1.36849509e+00,  1.16762083e+00,  9.33855372e-01,
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                  [-2.27003315e+00, -1.10069868e+00,  3.98783291e-01,
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                    1.24615961e+00,  2.25550470e+00, -6.75656023e-01,
                   -1.11414909e-01],
                  [ 8.21140477e-01, -1.33185780e+00,  1.22169051e+00,
                    3.80002096e-02, -7.51729597e-02,  1.03444120e+00,
                   -1.97207016e+00,  7.12305597e-01,  4.10324449e-01,
                    5.55044960e-01],
                  [ 2.11185169e-01,  2.36520096e-01, -1.18917054e-01,
                   -2.28831387e+00, -9.18688526e-01, -1.02463134e-01,
                   -2.85413088e-02, -4.61521607e-01,  6.74740245e-01,
                    7.32551867e-01],
                  [ 1.00696871e+00,  1.79600257e+00, -1.32575282e+00,
                   -9.50799489e-02, -2.94239437e-01,  3.54805118e-01,
                    1.36527665e+00,  1.14138655e+00,  2.07287100e+00,
                    4.89680827e-01],
                  [ 9.06678186e-01, -5.03963915e-02,  9.69587332e-01,
                   -1.48634225e+00,  1.02266029e+00,  9.74587466e-01,
                   -7.75634481e-01,  3.88701214e-01, -1.16272059e+00,
                   -6.11743272e-01],
                  [-3.24708968e-01,  1.97723253e+00, -2.84888355e-01,
                   -2.69155622e-01, -9.00368525e-01, -9.46357309e-01,
                    7.92271893e-01, -1.78797828e+00,  5.22554292e-01,
                    3.28287973e-01],
                  [-1.75433515e-01, -4.02731989e-01, -8.35777547e-01,
                   -1.23924490e+00, -7.45094880e-01, -3.62958625e-01,
                   -6.17577760e-01, -7.45443029e-01,  1.00633101e+00,
                    1.47806592e-01],
                  [ 1.18206842e+00, -4.41265819e-01, -5.52695549e-01,
                    1.24821668e+00, -1.18342574e+00, -1.68435014e+00,
                   -4.05792131e-01, -1.98258675e+00,  1.90486485e+00,
                   -1.21131318e+00],
                  [ 5.24400732e-01,  1.69054100e+00, -1.44944163e+00,
                   -2.05978323e+00, -1.93179858e-02,  3.43358325e-01,
                    5.73252501e-01,  1.17015345e+00,  7.24127569e-01,
                    3.02252091e+00],
                  [ 1.65248128e+00,  4.48576515e-01, -2.57531669e-01,
                    8.14246527e-01,  1.68982230e+00, -1.06541537e+00,
                    2.47867002e-01,  3.56131074e-02, -4.23980961e-01,
                    5.67601732e-01],
                  [ 8.32148755e-01,  1.33740082e+00, -5.29584025e-01,
                    5.63732674e-01,  8.22056969e-01,  2.42907319e-01,
                    2.46559886e-02, -2.16681856e-01, -7.31090551e-01,
                    7.80852007e-01],
                  [ 1.32244909e+00,  9.62937989e-01,  8.91502623e-01,
                    1.78943915e+00,  5.56834457e-02, -1.00555524e-01,
                   -4.33659410e-01,  1.21262355e+00, -1.08683510e+00,
                   -6.60560328e-01],
                  [-1.49634953e+00,  3.72195897e-01, -1.10987749e+00,
                   -1.76410054e+00,  2.86314601e+00, -7.95673232e-02,
                    1.15235872e+00,  1.35013385e+00,  1.12039305e-01,
                    8.49898341e-03],
                  [-1.52828123e+00,  4.27583708e-01,  1.98004180e-01,
                    1.47328065e+00, -3.98782156e-01,  3.77725692e-01,
                   -1.55867393e+00, -1.16604085e+00, -2.63226788e-01,
                   -7.73535263e-01],
                  [ 8.16420246e-01,  2.35213905e+00,  1.19606515e+00,
                    2.32834041e-02, -3.05890149e-02, -1.42108994e+00,
                   -4.40825488e-01, -6.90008024e-01, -2.29994717e+00,
                    9.44161941e-02],
                  [ 1.04431131e+00,  2.05158538e+00,  1.77792911e-01,
                   -1.15639801e+00, -1.16879575e+00, -1.50927009e-01,
                   -9.82331555e-02,  2.07021953e+00,  1.25097281e+00,
                   -5.56746559e-01],
                  [ 1.40699915e+00, -6.21317077e-01, -1.21274438e+00,
                   -3.17789976e-01, -6.05525347e-01, -1.66554119e+00,
                   -2.24207857e-01,  2.86311630e-01,  1.62249173e+00,
                   -3.15283909e-01],
                  [-2.22061713e-01,  8.03942643e-01,  1.97668919e-01,
                   -8.55866643e-01,  9.88830867e-02, -1.70861777e+00,
                   -3.67899753e-01, -7.61882907e-01, -9.87186951e-01,
                    8.70674901e-01],
                  [ 5.04680050e-01,  9.08143447e-01,  3.49483543e-01,
                    5.26629508e-01, -1.52242313e-01, -2.51796334e-01,
                   -1.88596631e-01,  8.97122390e-02, -1.93901287e+00,
                    4.62145013e-01],
                  [-1.08750323e+00,  6.96678417e-01,  1.67642553e+00,
                    9.51789049e-01,  6.18442059e-01,  4.20069032e-01,
                   -8.84441493e-02, -5.02794661e-01,  7.34871358e-01,
                   -3.70167361e-01],
                  [ 1.02534311e-02, -9.24318196e-01, -5.51238983e-01,
                    4.41497064e-01, -1.45156214e+00, -1.44392990e-01,
                    1.23557562e+00, -3.63257473e-01, -1.06689503e+00,
                   -7.69817492e-01],
                  [ 1.02433650e+00, -7.36088937e-01,  1.02813190e+00,
                   -8.88377348e-01, -2.65042624e-01,  1.75908034e+00,
                    1.17759944e+00, -2.52734331e-01,  1.07444102e+00,
                   -1.24722114e+00],
                  [ 1.01478705e+00, -1.24395612e+00,  4.35237720e-01,
                   -1.70794994e-01,  8.02030212e-01, -1.72495422e+00,
                    1.26133253e+00,  8.94681186e-01, -1.40398825e+00,
                   -1.20863522e+00],
                  [-8.17745312e-02,  1.08892670e+00, -1.20220921e+00,
                   -7.66254557e-01,  4.67619816e-01,  2.92867238e-01,
                    3.34066366e-01,  2.72157563e-01,  6.24135785e-01,
                   -7.54899145e-01],
                  [ 1.45617099e+00,  1.66893844e+00, -5.58569215e-01,
                   -1.84745386e+00, -3.97209120e-01, -7.59556720e-01,
                   -4.16718680e-01, -5.85617043e-01, -1.92122540e-01,
                    3.07005197e-01],
                  [-4.16143417e-01,  3.00432408e-01, -2.15786999e-01,
                   -6.71918241e-01,  8.03132199e-01,  1.12905263e+00,
                   -4.78372378e-01,  2.27117346e-01, -8.37517704e-01,
                    3.16726497e-01],
                  [-2.28093936e+00, -4.81176088e-01, -7.76808530e-01,
                   -5.80287723e-01,  9.54935457e-01, -7.01360347e-01,
                    4.48368466e-01, -1.51902492e-01,  2.74335441e-01,
                    3.39502195e-01],
                  [ 1.46230790e+00,  2.30933699e+00, -1.52025190e+00,
                    4.17092247e-01,  1.94095135e+00, -1.94548496e+00,
                    1.27732457e+00,  6.06274737e-01,  1.30848585e+00,
                   -9.14296391e-01],
                  [-1.42496277e-01,  5.56228852e-01,  1.59415730e+00,
                    6.31585480e-01,  7.98419866e-01,  2.16748128e-01,
                   -2.59198110e-01, -6.94802408e-03,  1.56305458e+00,
                   -3.83728709e-01],
                  [-1.27225106e+00,  5.12705111e-01, -2.18685041e-03,
                    3.08420413e-01, -8.56867924e-01, -2.29866378e+00,
                    1.87798641e-01,  2.04782145e-02, -4.42340787e-01,
                    1.94318228e+00],
                  [-1.60618804e-01,  1.13947332e+00,  2.04588233e-01,
                   -4.97407503e-01,  3.53797043e-02, -6.91517388e-01,
                   -1.60955398e+00,  8.54010939e-01,  1.94273349e+00,
                    1.17465363e+00],
                  [-8.24845092e-01,  6.23131743e-01,  2.05627626e+00,
                   -9.10928865e-02,  1.56120445e+00,  8.84370639e-01,
                   -8.19393246e-01, -8.01984250e-01, -9.86370368e-02,
                    1.08884622e+00],
                  [-1.35943099e+00, -1.17173264e-01, -1.76507193e+00,
                   -9.22582492e-01,  7.32594020e-01, -1.25723253e-01,
                   -1.18067363e+00,  9.87389196e-01, -8.38230045e-01,
                   -1.49159808e+00],
                  [-5.16406769e-01,  3.13915725e-01, -8.54823809e-01,
                   -1.02470557e+00,  1.21560450e+00,  9.20955146e-01,
                   -1.09237377e+00,  5.84158500e-01, -1.16055340e+00,
                    8.37327161e-02],
                  [ 8.65162098e-01, -5.05677085e-01,  1.82949868e-01,
                   -5.92753364e-01, -5.62332911e-01, -1.08210662e-01,
                   -1.31862879e+00,  1.03101919e+00,  7.38045897e-02,
                   -4.71621984e-01],
                  [ 7.83383547e-02,  1.91456640e+00, -9.74402295e-01,
                    1.55854320e+00,  2.59809274e+00,  7.83316418e-02,
                   -1.40941942e+00,  1.19892060e+00, -9.31637829e-01,
                   -3.53693428e-02],
                  [ 7.17526486e-01, -9.69508312e-01,  3.24199919e-01,
                   -8.95324253e-01, -1.03194979e+00, -4.32445892e-01,
                   -4.33561500e-01,  3.21475394e-01,  3.68854551e-01,
                    1.08531537e+00],
                  [-4.15527077e-01, -5.16091939e-01,  3.99410114e-01,
                    4.63791972e-02,  1.37200838e+00, -1.17613794e+00,
                    3.54701520e-01,  9.20563172e-01,  6.19535628e-01,
                   -2.73494371e-01],
                  [-1.28388793e+00,  2.01759201e-01,  2.40823245e+00,
                   -6.14183274e-01, -2.10437195e-01,  9.40762801e-01,
                    1.00825258e+00,  1.01788415e+00, -8.42117567e-02,
                   -3.20454626e+00],
                  [-1.42784282e+00,  9.84805601e-01,  6.40402245e-01,
                   -5.69869434e-01,  4.37650067e-01,  9.12624333e-01,
                   -9.61378102e-01, -1.04562022e+00, -1.67912791e+00,
                    3.76781052e-01],
                  [-6.60135138e-01, -2.18287191e+00, -4.93030369e-01,
                   -1.76235979e-01,  9.35579631e-01,  1.64793682e-01,
                   -1.40587603e+00, -6.81806964e-01,  1.02215879e+00,
                    4.31489160e-01],
                  [ 1.62515156e-01,  9.15907575e-01,  1.15927657e+00,
                   -8.10727657e-01,  2.78226054e-01,  1.42864561e-01,
                   -8.35643232e-01,  1.64703107e-01, -1.34467718e+00,
                   -8.68861845e-01],
                  [-2.44030875e-01, -3.66378408e-01, -1.10882172e+00,
                   -9.86625978e-01, -9.90647599e-01, -1.93271978e+00,
                    3.19268525e-01,  6.24626362e-01,  4.23577939e-01,
                   -3.05202156e-01],
                  [-6.60997240e-01, -8.21343516e-01, -1.02020096e-01,
                    2.31683252e-01,  4.95402344e-01, -3.08681280e-01,
                   -9.60064049e-01,  4.74289652e-01,  4.29826030e-01,
                   -3.02252591e-01],
                  [ 1.32019648e+00, -1.42493591e+00,  1.00049789e+00,
                    1.74671065e+00,  9.75798761e-01,  1.08280211e+00,
                    1.66381266e+00,  4.79047112e-01,  1.02944596e+00,
                    1.44188697e+00],
                  [ 1.41356761e+00, -1.29860859e+00,  3.21765217e-01,
                    1.37592461e+00, -2.28733972e-01,  6.07310301e-01,
                   -9.91045263e-01, -1.13200899e-01,  1.14816888e+00,
                   -5.85060490e-01],
                  [ 7.87384986e-01,  1.02690164e-01,  7.30967387e-01,
                    1.55640681e+00,  3.66062745e-01,  8.35093179e-01,
                   -9.52345842e-01, -4.77972470e-01,  1.72310542e+00,
                   -2.62599445e-01],
                  [-8.01348275e-01, -4.17957485e-01, -1.30991555e+00,
                   -2.65776168e-01, -4.23852828e-01,  7.86504260e-01,
                   -1.30354920e-02,  1.48565581e-01, -1.14283710e-01,
                    9.29870682e-01]]])
        • c
          (chain, draw, c1, c2)
          float64
          -1.969 -0.3835 ... -0.6989 -0.393
          array([[[[-1.9685806 , -0.38345697, -1.14734465, -0.08337334],
                   [ 0.769021  ,  1.11133546,  1.91498295, -0.46834211],
                   [-0.23264243, -1.05010379, -2.14064243, -1.07390044]],
          
                  [[-0.3422121 ,  0.11486382, -0.24465889,  0.18087892],
                   [-0.0338139 , -0.60712889,  0.07562642,  0.56905369],
                   [-0.18189297,  1.7870949 , -1.57350046, -0.50810089]],
          
                  [[-0.0510513 , -0.36662106, -0.8270934 , -1.26042414],
                   [ 0.93017305,  0.65638302,  2.30087812, -0.57078071],
                   [-0.56215181,  1.19480847,  1.10890094, -0.87102009]],
          
                  ...,
          
                  [[ 0.40663338,  0.5611835 ,  0.39908726, -0.29270602],
                   [ 0.58947034,  0.26671407, -0.57288192, -0.50354393],
                   [ 1.51137947,  0.09171223, -0.91077266,  0.2399483 ]],
          
                  [[-1.46379518, -1.87590622,  0.51953765, -0.10717415],
                   [ 1.32766471,  0.0645871 ,  0.0359231 ,  2.3641054 ],
                   [ 0.64254228,  0.77359929,  0.08771938,  0.93903909]],
          
                  [[-1.04082777,  0.17818282,  0.27089952, -1.47930329],
                   [ 0.29680156,  0.64995149, -0.5202781 , -0.01071339],
                   [-0.551221  , -0.40814589, -0.69886247, -0.39295165]]]])
      • created_at :
        2020-06-10T18:19:03.966946
        arviz_version :
        0.8.3

From PyMC3

[2]:
import pymc3 as pm

draws = 500
chains = 2

eight_school_data = {
    "J": 8,
    "y": np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
    "sigma": np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}
[7]:
with pm.Model() as model:
    mu = pm.Normal("mu", mu=0, sd=5)
    tau = pm.HalfCauchy("tau", beta=5)
    theta_tilde = pm.Normal("theta_tilde", mu=0, sd=1, shape=eight_school_data["J"])
    theta = pm.Deterministic("theta", mu + tau * theta_tilde)
    pm.Normal(
        "obs", mu=theta, sd=eight_school_data["sigma"], observed=eight_school_data["y"]
    )

    trace = pm.sample(draws, chains=chains)
    prior = pm.sample_prior_predictive()
    posterior_predictive = pm.sample_posterior_predictive(trace)

    pm_data = az.from_pymc3(
        trace=trace,
        prior=prior,
        posterior_predictive=posterior_predictive,
        coords={"school": np.arange(eight_school_data["J"])},
        dims={"theta": ["school"], "theta_tilde": ["school"]},
    )
pm_data
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [theta_tilde, tau, mu]
100.00% [2000/2000 00:02<00:00 Sampling 2 chains, 3 divergences]
There were 3 divergences after tuning. Increase `target_accept` or reparameterize.
100.00% [1000/1000 00:01<00:00]
[7]:
arviz.InferenceData
    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 2
        • draw: 500
        • school: 8
        • chain
          (chain)
          int64
          0 1
          array([0, 1])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 495 496 497 498 499
          array([  0,   1,   2, ..., 497, 498, 499])
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • mu
          (chain, draw)
          float64
          6.638 4.791 5.564 ... 5.818 2.299
          array([[ 6.63799683e+00,  4.79134072e+00,  5.56424218e+00,
                   5.57420954e+00,  3.22669739e+00,  4.09925197e+00,
                   6.77486926e+00,  7.78605439e+00, -2.52944163e-01,
                   6.61229871e+00,  4.18502958e+00,  1.76376618e+00,
                   4.62694426e+00,  3.50036596e+00,  3.05630576e+00,
                   6.62692262e+00,  4.14235573e+00,  6.16275502e+00,
                   6.22938258e+00,  6.15304590e+00,  3.22079869e+00,
                   7.23136829e-01,  7.23136829e-01,  5.34538848e+00,
                   2.39661416e+00,  3.69046096e+00,  2.48955251e+00,
                   7.46552620e+00,  9.03574415e+00,  6.72969686e+00,
                   6.34335555e+00,  4.04220266e+00,  2.19778203e+00,
                   1.37076499e-02,  1.74828963e+00,  7.67516122e+00,
                   7.67516122e+00,  6.85639862e+00,  4.64813775e+00,
                   2.65791301e+00,  5.01452937e+00,  1.83039053e+00,
                   1.78045535e+00,  2.17111590e+00,  2.00686198e+00,
                   5.41209154e+00,  4.34875837e+00,  4.91332931e+00,
                   3.53930002e+00,  7.51604256e+00,  7.19161274e+00,
                   2.03515930e+00,  9.42214963e+00,  7.09555156e+00,
                   1.93087165e+00,  5.59001258e+00,  7.17291829e+00,
                   5.13261847e+00,  5.86915693e+00,  2.57897255e+00,
                   6.61818370e+00,  1.39310780e+00,  3.59564785e+00,
                   4.32735112e+00,  7.85800197e+00,  1.60693679e+00,
                   5.56027445e+00,  7.71824903e+00,  7.52958298e+00,
                   2.17221759e+00,  2.61447368e+00,  1.35683982e+01,
                   9.20871183e-02,  3.19997426e+00,  4.76437822e+00,
                   5.54460105e+00,  6.67417392e+00,  5.16285638e+00,
                  -8.19217157e-01,  1.26674178e+01, -5.89391857e-01,
                  -5.89391857e-01, -2.70426811e+00,  9.43770323e+00,
                   1.01234303e+01,  1.54012544e+00,  1.75412845e+00,
                   4.47119156e+00,  4.97567517e+00,  1.84977782e+00,
                   6.91461195e+00,  6.60657308e+00,  3.56008090e-01,
                   6.93045204e+00, -1.25531329e-01, -1.25531329e-01,
                   6.39259731e-01,  7.94587362e+00,  2.63018477e+00,
                   5.63533128e+00,  3.86413926e+00,  4.56795589e+00,
                   9.47234622e+00,  2.10143003e+00,  6.41839518e+00,
                   3.83593844e+00,  8.59218468e+00,  2.27599500e+00,
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                   5.33441030e+00,  6.17361730e+00,  4.54183205e+00,
                   7.69989749e+00,  4.80206324e+00,  7.78484647e+00,
                   9.13084163e+00,  7.74409223e+00,  1.82635576e+00,
                   6.35534631e+00,  5.51578307e+00,  8.54587017e+00,
                   7.07142066e+00, -1.74591256e+00,  6.07298566e+00,
                   6.51718847e+00,  6.09250191e+00,  3.30503182e+00,
                   7.06191823e+00,  1.74290159e+00, -1.98884819e-01,
                   8.65279028e+00,  1.57669468e+00,  6.61965150e+00,
                   3.78306891e+00,  1.23508683e+00,  9.96743433e+00,
                   6.49423794e+00,  1.59359178e+00,  5.36302901e+00,
                   4.75614082e+00,  4.29573654e+00,  2.63409767e+00,
                   4.40955601e+00,  4.34868292e+00, -2.90253461e+00,
                   8.98542517e+00,  8.50190640e+00,  6.91148998e+00,
                   4.97370711e+00,  3.87222569e+00,  4.60253064e+00,
                   3.96983634e+00,  5.22072459e+00,  7.60356156e+00,
                   5.93296293e+00,  6.33904667e+00,  5.19974188e-01,
                   1.04765948e+00,  7.75246391e+00,  1.63434051e+00,
                   6.95600941e+00,  4.19189702e+00,  1.71096157e+00,
                  -1.45331205e-01, -4.12236921e+00,  4.13136383e+00,
                   2.35654371e+00,  4.04759451e+00,  2.24641101e+00,
                   3.43184094e+00,  7.77176280e-01,  2.14958654e+00,
                   4.88253287e+00,  8.46948671e-01,  5.88180081e+00,
                   2.97002637e+00,  5.46509743e+00,  4.16808395e+00,
                   3.89340051e+00,  3.29571881e+00,  6.14736550e+00,
                   9.77643381e+00,  8.45758710e+00,  3.69314826e+00,
                   5.23777084e+00,  5.06487836e+00,  5.49293805e+00,
                   5.78370575e+00,  4.89747489e+00,  2.06910849e+00,
                   7.60068455e+00, -1.37740697e+00,  1.00020645e+01,
                  -1.76905089e-01,  1.00654596e+01,  7.98446662e+00,
                   8.79308803e+00, -1.28267861e-01,  9.29732175e+00,
                   1.01750150e+01,  4.96500994e+00,  5.21273557e+00,
                   1.39171806e+00,  9.49000305e+00,  5.49988414e-01,
                   7.33288112e+00,  5.17975767e+00,  4.67842691e+00,
                   4.80755480e+00,  6.58545056e-01,  8.13979759e+00,
                   4.89660451e+00,  6.35332576e+00, -4.69844004e+00,
                   8.97627606e+00,  4.57590275e+00,  5.93302017e+00,
                   4.74157220e+00,  4.37346125e+00,  5.06694948e+00,
                   2.19646582e+00,  5.56067421e+00,  3.04828461e+00,
                   5.92827468e+00,  6.21724225e+00,  2.51280189e+00,
                   9.57306721e+00,  7.59353227e+00,  2.09202476e+00,
                   9.88059803e+00,  4.54680518e+00, -4.30483067e+00,
                   8.92024468e+00,  1.26309327e+00,  9.46959872e+00,
                  -1.17827288e+00, -3.66655282e-01, -9.16874577e-01,
                   6.03922031e+00,  1.88068890e+00,  5.80097792e+00,
                   4.10859484e+00,  7.52813003e+00, -1.11027182e-01,
                   1.37308819e+00,  1.19388966e+00,  8.58912431e-03,
                   2.22575099e+00,  7.20720195e+00,  5.48023988e+00,
                   1.28400000e+00, -2.20449686e-01,  5.18856371e+00,
                   6.01845550e+00,  4.77155051e+00,  4.18297145e+00,
                   5.43830940e+00,  2.46429298e+00,  7.28660900e+00,
                   7.21764793e+00,  5.36153164e+00,  5.04585974e+00,
                   1.40262626e+00,  1.40262626e+00,  7.26603051e+00,
                   2.59531892e+00,  6.01218155e+00,  6.23284317e+00,
                   2.91248685e+00,  5.84996530e+00,  7.94833070e+00,
                   5.81831499e+00,  2.29860647e+00]])
        • theta_tilde
          (chain, draw, school)
          float64
          -0.3253 -0.6165 ... 1.222 0.2978
          array([[[-0.32529772, -0.61651454, -0.1667071 , ...,  1.03328716,
                    2.1823746 ,  0.47316842],
                  [ 2.02958114,  1.38140157,  0.75320748, ..., -0.76415401,
                   -0.26376613,  2.59527651],
                  [-1.29974382, -0.93838206, -1.66930843, ...,  0.45610521,
                    1.16510883, -1.90862339],
                  ...,
                  [ 0.76405243,  1.57497136, -0.19382101, ..., -0.90719718,
                    0.13818502, -0.53287742],
                  [-0.01956823, -0.44742285,  0.22391893, ...,  1.26672305,
                    1.48674961,  0.59971362],
                  [-1.31647166,  0.85301164,  0.48705457, ...,  1.10464535,
                   -0.20971009,  0.16073751]],
          
                 [[ 0.39528795,  2.42188047, -0.63226669, ..., -1.08800486,
                   -1.18916527, -1.15738863],
                  [-1.14188208,  1.13112039,  0.07025925, ..., -0.71775304,
                    0.42484354,  0.43962524],
                  [ 0.71622022, -1.36901772,  0.34158932, ...,  1.14499937,
                   -0.08757469, -1.25347347],
                  ...,
                  [ 0.18628521,  1.50088211, -0.65171658, ...,  0.48396343,
                    0.77830976, -0.36442883],
                  [ 0.86143906, -1.5081053 ,  0.16205563, ..., -1.43705565,
                   -0.382151  , -0.01870404],
                  [ 0.70965545,  1.59856161, -0.47552168, ...,  0.91627404,
                    1.22218512,  0.29782471]]])
        • tau
          (chain, draw)
          float64
          3.1 1.632 1.529 ... 2.741 4.724
          array([[3.09988894e+00, 1.63207672e+00, 1.52902197e+00, 2.30099852e+00,
                  8.31268078e-01, 1.88898817e+00, 5.85874168e+00, 4.71824548e+00,
                  2.36699580e+00, 2.34732021e+00, 2.05737377e+00, 2.22388599e+00,
                  1.26633038e+00, 3.10758565e+00, 2.43266266e+00, 2.49894565e+00,
                  3.62801031e+00, 2.66434647e+00, 6.03401501e+00, 4.20103917e+00,
                  2.87235863e+00, 9.61176630e+00, 9.61176630e+00, 4.47341001e+00,
                  5.66040767e+00, 9.82792942e-01, 1.62994744e+00, 6.81143684e+00,
                  1.42101541e+00, 3.99436157e+00, 1.06113735e+00, 6.66151684e+00,
                  1.44678348e+00, 9.29213043e-01, 6.00298896e-01, 8.65854134e+00,
                  8.65854134e+00, 7.49195541e+00, 3.92008212e-01, 4.67262667e-01,
                  1.14031719e+01, 1.91770387e-01, 1.13407014e-01, 2.31341743e-01,
                  1.87226273e+01, 3.07049024e-01, 3.79160657e+00, 2.29027053e+00,
                  4.54164481e+00, 3.06000216e+00, 1.61702924e+00, 1.42514668e+00,
                  2.69966316e+00, 7.76593714e+00, 9.35329781e-01, 4.80484917e+00,
                  4.60629543e-02, 3.78059536e-02, 1.46668064e-01, 7.85845041e-02,
                  2.45290474e+00, 3.99644466e+00, 2.81231960e+00, 3.45085186e+00,
                  1.00796319e+00, 2.72362547e+00, 1.61928447e+00, 2.86957381e+00,
                  3.01123031e+00, 7.49851917e-01, 9.57235307e-01, 2.35480165e+00,
                  9.53584743e+00, 1.50321215e+00, 8.66088994e+00, 3.95555017e+00,
                  8.28477536e-01, 1.16039960e+00, 5.29813451e+00, 1.82651411e-01,
                  1.50293359e+01, 1.50293359e+01, 1.70908463e+00, 4.49037167e+00,
                  3.72729985e+00, 4.20267362e-02, 2.15497907e-01, 1.44651372e-01,
                  8.97409661e+00, 3.95659504e+00, 1.74384378e+00, 3.01505721e+00,
                  8.89669163e+00, 6.33618449e+00, 3.36126815e+00, 3.36126815e+00,
                  1.03556605e+01, 8.41171251e-01, 3.08236370e+00, 7.71365841e+00,
                  3.40615951e+00, 5.29949043e+00, 3.89052725e+00, 2.97310920e-01,
                  3.79674976e-01, 5.40723457e+00, 3.21220675e-01, 3.39422976e+00,
                  5.62340485e+00, 7.33074407e+00, 2.03764109e+00, 5.68137917e+00,
                  5.68137917e+00, 2.83686052e+00, 4.91676473e+00, 6.62090533e+00,
                  6.64313421e+00, 3.60767832e+00, 2.64339476e+00, 5.23419542e+00,
                  6.54119359e-01, 9.90659523e-01, 1.26385767e+00, 9.46167070e-01,
                  3.42942204e+00, 1.17157162e+01, 1.51882166e+00, 7.75894868e+00,
                  1.86186982e+00, 1.05676321e+01, 8.81156578e+00, 2.97112722e+00,
                  4.97560335e+00, 4.97560335e+00, 2.37615802e+00, 4.85582620e-01,
                  1.75115034e-01, 2.24492144e-02, 5.19194864e-03, 2.44152982e-03,
                  4.96016077e-04, 9.81960781e-04, 2.61456184e-01, 3.04503815e+00,
                  1.49740455e+00, 3.09210525e+00, 2.38372922e+00, 1.07710929e+00,
                  7.37178789e-01, 1.44477609e+00, 4.44958349e-01, 7.56283868e+00,
                  1.30693621e+01, 6.00919393e+00, 3.27627074e+00, 3.27627074e+00,
                  3.61464843e+00, 1.42101331e+00, 4.23921964e-01, 8.45466943e+00,
                  4.63349584e+00, 4.46047362e+00, 8.78396465e+00, 3.68844510e+00,
                  6.55355892e+00, 2.16129532e+00, 2.77333940e+00, 3.76898084e+00,
                  9.47836834e-01, 1.15779865e+00, 1.08542059e+01, 7.84930686e-01,
                  2.53342726e+00, 9.22488199e-01, 6.24873580e+00, 6.24873580e+00,
                  5.37298831e+00, 2.12673184e+00, 1.43190109e+00, 3.72911093e+00,
                  1.67789722e+00, 4.10229845e+00, 2.91020442e+00, 4.75219278e+00,
                  2.05454858e+00, 7.02387879e+00, 1.92291069e+00, 3.57246023e-01,
                  2.83701174e+00, 7.95061579e+00, 3.87302365e+00, 6.27845736e+00,
                  7.65529077e-01, 2.85486857e+00, 4.27274083e+00, 1.63762758e+00,
                  7.98990100e-01, 1.20889927e+00, 3.59308318e+00, 3.23508196e+00,
                  5.48955086e+00, 3.47140380e+00, 3.47140380e+00, 2.14376772e+00,
                  5.27427110e-01, 3.29333098e+00, 1.75016375e+00, 1.22541172e+00,
                  1.15733505e+01, 1.15733505e+01, 2.77463974e+00, 3.07338819e+00,
                  3.07338819e+00, 1.70827704e+00, 4.18041312e+00, 7.70963663e-01,
                  8.35031192e-01, 6.53935957e+00, 3.63566215e-01, 9.72246066e+00,
                  1.40166669e+00, 3.38578921e+00, 3.07436946e+00, 9.76477570e-01,
                  2.11253628e+00, 2.11351930e+00, 2.46627791e-01, 1.65123263e+00,
                  1.29966369e+00, 2.56888919e+00, 1.00424894e+01, 3.52674417e+00,
                  6.82369555e+00, 2.63738500e+00, 7.83608447e+00, 2.70102342e+00,
                  4.45264351e+00, 3.08078679e-01, 4.49708000e+00, 9.99135072e+00,
                  3.55835310e+00, 1.16907517e+00, 2.02513622e+00, 1.02567962e-01,
                  5.16058441e+00, 6.94456578e-01, 3.04556772e+00, 8.53439537e+00,
                  4.36448122e+00, 4.36448122e+00, 2.58496665e+00, 1.00182772e+00,
                  3.81383379e+00, 3.74173366e+00, 4.48486880e+00, 2.82288845e+00,
                  7.22636068e-01, 3.56734285e+00, 1.67506117e+00, 2.02941736e+00,
                  4.12335849e+00, 7.57508195e+00, 3.25739237e+00, 3.14910194e+00,
                  4.83292307e+00, 3.78441995e+00, 1.01299820e+00, 1.98906741e+00,
                  3.41574334e+00, 2.06843286e+00, 1.55608621e+00, 1.92423040e-01,
                  5.08025259e+00, 6.16125429e+00, 7.36498515e-01, 1.24789864e+00,
                  6.27956089e+00, 6.27956089e+00, 7.49902395e-01, 2.11452399e+00,
                  2.24293487e-01, 3.35055904e-01, 1.68753300e-02, 4.18807137e-01,
                  4.58889059e+00, 1.54259092e+00, 1.03803681e+00, 5.31534450e+00,
                  2.60984305e+00, 2.99648210e+00, 4.91208069e+00, 9.90204033e+00,
                  1.35299652e+00, 8.37925328e+00, 3.34839656e+00, 5.28114427e+00,
                  2.21231385e+00, 7.81986140e-01, 2.68384539e+00, 1.82893404e+00,
                  2.51582305e+00, 2.22615720e+00, 7.25987045e+00, 8.99140943e+00,
                  8.99140943e+00, 7.81139000e+00, 4.75357076e+00, 9.80665484e-01,
                  6.26918311e-01, 4.63030324e-02, 7.68659875e-01, 2.10636907e+00,
                  5.41121322e+00, 9.55072350e-01, 3.78895489e+00, 1.53556405e+00,
                  1.36718670e+00, 5.32069899e+00, 5.32069899e+00, 2.10949104e+00,
                  2.10949104e+00, 4.48217733e+00, 3.45878976e+00, 5.23224937e+00,
                  7.23491941e-01, 1.09630159e+01, 1.90895106e+00, 1.94941130e+00,
                  8.02391448e+00, 2.85057302e+00, 5.51741597e+00, 2.33330862e+00,
                  5.63950929e+00, 2.00352029e+00, 4.18123136e+00, 7.96439656e+00,
                  1.25523482e+00, 4.27480930e+00, 8.66754251e-01, 1.33945808e+00,
                  1.96201914e+00, 1.33772085e+00, 1.78255793e+00, 2.23659524e+00,
                  1.94135128e+00, 2.79944847e+00, 1.10391683e-01, 1.56316513e+00,
                  3.72869234e+00, 9.55436772e-01, 2.13150808e+00, 4.47963252e+00,
                  3.78356295e+00, 5.10899353e-01, 4.26619097e+00, 1.87941457e+01,
                  1.87941457e+01, 3.77009222e+00, 6.41488833e-01, 6.80390052e-01,
                  1.99263496e+00, 5.13747821e+00, 5.13747821e+00, 3.14078111e+00,
                  5.88111221e+00, 3.29812183e+00, 5.75164624e+00, 2.69121554e+00,
                  1.56347605e+00, 5.27496678e+00, 2.87100899e+00, 2.31302906e+00,
                  1.68828031e+00, 1.09680422e+00, 2.91573241e-01, 1.42346712e+00,
                  9.79412468e-01, 3.49815706e+00, 4.95950372e+00, 7.14087628e+00,
                  1.62857484e+01, 4.72245450e-01, 5.43036556e+00, 3.80175888e-01,
                  2.74008719e-01, 5.03512295e-01, 2.38120067e+00, 3.01954806e-01,
                  2.33082112e-01, 6.65830660e-02, 3.33221349e+00, 1.93945827e+00,
                  3.12383685e+00, 8.70943321e+00, 1.52682644e+00, 3.68808675e+00,
                  5.24348750e+00, 1.95509466e+00, 3.66047354e+00, 5.97797944e+00,
                  5.97797944e+00, 7.97725643e-01, 1.44672287e+00, 1.86453076e+00,
                  2.15691321e+00, 1.40205795e+00, 1.28605987e+00, 6.35787524e+00,
                  3.15948844e+00, 1.94095239e+00, 8.69195133e+00, 8.38406149e-01,
                  5.38691304e+00, 1.15395625e+00, 9.96413349e-01, 4.18266814e+00,
                  3.76753069e+00, 1.38748987e+00, 4.47522270e+00, 1.59775810e+00,
                  2.60969544e+00, 2.33253345e-01, 2.34764683e+00, 1.44320625e+00,
                  3.33586202e+00, 4.94987324e+00, 4.97271936e+00, 2.10739974e+00,
                  2.33071428e+00, 6.63438674e-01, 4.57847467e+00, 2.01055839e+00,
                  3.69642715e+00, 1.17259406e+01, 1.17259406e+01, 3.66305533e+00,
                  8.64030696e-01, 2.50151607e+00, 9.32171449e+00, 4.08032473e+00,
                  4.08032473e+00, 1.77127432e+00, 1.16114849e+01, 1.31348481e+00,
                  9.71958059e-01, 3.26610629e+00, 9.46118073e+00, 5.62409928e+00,
                  6.30274536e+00, 5.42199958e+00, 1.34460486e+01, 1.34460486e+01,
                  2.41417679e+00, 3.57253639e+00, 3.57253639e+00, 9.10126440e+00,
                  6.56418646e+00, 1.31892758e+00, 1.71368899e+00, 3.49349047e+00,
                  3.22679402e+00, 3.22679402e+00, 5.40345503e+00, 1.01589129e+01,
                  4.15664338e-02, 2.18942477e-02, 2.86514992e-02, 2.21497457e-02,
                  1.79285582e+01, 1.52018745e-01, 2.01387018e+00, 5.44963070e-02,
                  4.47199619e-02, 8.83507675e-01, 1.80266425e+00, 1.90345940e+00,
                  2.63387518e-01, 2.40564145e+00, 9.87268294e-01, 3.78376592e+00,
                  6.91571313e-01, 7.74075349e+00, 7.85526840e-01, 5.25342514e+00,
                  2.59837379e+00, 3.78014832e+00, 1.65762665e+00, 2.03766737e+00,
                  9.48164296e+00, 3.18067452e+00, 8.12671270e+00, 4.65211529e+00,
                  1.35087314e+01, 7.04136640e+00, 1.79561310e+00, 1.30703893e+00,
                  5.40688975e+00, 2.92931379e+00, 1.50542743e+00, 5.34863668e+00],
                 [1.24679522e+00, 2.69730666e+00, 3.06708473e+00, 6.92341103e+00,
                  7.26717041e+00, 9.72414460e+00, 1.35577385e+00, 1.82326047e+00,
                  3.96073369e+00, 1.81744113e+00, 3.72269348e+00, 4.77067056e+00,
                  1.56675436e+00, 1.02068900e+00, 4.81841901e+00, 9.12498146e+00,
                  7.25951080e-02, 1.10271479e+01, 7.45875275e+00, 2.88800003e-01,
                  1.81995149e-01, 5.12095187e+00, 9.87610764e-01, 3.69307794e+00,
                  4.84798220e+00, 4.77871157e+00, 9.68037949e-01, 3.06196230e+00,
                  1.15477283e+00, 6.61843048e+00, 5.59888635e+00, 4.14011897e+00,
                  2.86431779e+00, 2.42811202e+00, 4.20164971e+00, 1.70820078e+00,
                  3.75174586e+00, 3.37788148e+00, 5.25038077e+00, 2.60211647e+00,
                  8.50346222e-01, 1.60489849e+00, 6.17231562e+00, 2.05356030e+00,
                  8.92248648e+00, 1.06028349e+00, 2.38133402e+00, 2.00470276e+00,
                  4.26467659e+00, 9.47934506e-01, 2.76079372e+00, 1.41926392e+00,
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          (chain, draw, school)
          float64
          5.63 4.727 6.121 ... 8.072 3.706
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                 [[ 5.32205148,  7.84879735,  4.04090126, ...,  3.47268908,
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      • created_at :
        2020-06-10T18:19:23.327079
        arviz_version :
        0.8.3
        inference_library :
        pymc3
        inference_library_version :
        3.8

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 2
        • draw: 500
        • obs_dim_0: 8
        • chain
          (chain)
          int64
          0 1
          array([0, 1])
        • draw
          (draw)
          int64
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          array([  0,   1,   2, ..., 497, 498, 499])
        • obs_dim_0
          (obs_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • obs
          (chain, draw, obs_dim_0)
          float64
          15.57 12.1 3.026 ... 18.62 -10.4
          array([[[ 15.56955881,  12.10362895,   3.0259356 , ...,   5.25677454,
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                  ...,
                  [-11.94803447,   0.0896506 ,  28.35944418, ...,  -1.47988496,
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                 [[ -0.71864835, -14.63818199, -27.80108664, ...,   3.88081011,
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                    19.94187807, -14.3233147 ],
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                  [ 29.8775133 ,   5.52945089,   3.75273982, ...,   7.82224107,
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      • created_at :
        2020-06-10T18:19:23.476419
        arviz_version :
        0.8.3
        inference_library :
        pymc3
        inference_library_version :
        3.8

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 2
        • draw: 500
        • obs_dim_0: 8
        • chain
          (chain)
          int64
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          array([0, 1])
        • draw
          (draw)
          int64
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        • obs_dim_0
          (obs_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • obs
          (chain, draw, obs_dim_0)
          float64
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                 [[-4.76985395, -3.22163794, -3.78835204, ..., -3.34209906,
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      • created_at :
        2020-06-10T18:19:23.474654
        arviz_version :
        0.8.3
        inference_library :
        pymc3
        inference_library_version :
        3.8

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 2
        • draw: 500
        • chain
          (chain)
          int64
          0 1
          array([0, 1])
        • draw
          (draw)
          int64
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        • energy
          (chain, draw)
          float64
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        • step_size_bar
          (chain, draw)
          float64
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        • mean_tree_accept
          (chain, draw)
          float64
          1.0 0.4507 1.0 ... 0.9712 0.9935
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                  9.00291538e-001, 5.66389903e-001, 8.24410013e-001,
                  6.15006553e-001, 9.34125384e-001, 9.78014054e-001,
                  9.50952365e-001, 9.83545650e-001, 7.95749396e-001,
                  1.00000000e+000, 3.53488352e-001, 7.95919188e-001,
                  9.29582196e-001, 4.63259736e-001, 5.60765398e-001,
                  5.53202503e-001, 9.36517087e-001, 7.20815029e-001,
                  9.95465870e-001, 9.79275407e-001, 6.65296183e-001,
                  9.07598721e-001, 7.09201638e-001, 7.56545069e-001,
                  9.00612778e-001, 2.69444132e-001, 1.00000000e+000,
                  9.15262486e-001, 5.48248061e-001, 9.81737093e-001,
                  9.28301202e-001, 9.95322426e-001, 4.80986802e-001,
                  8.86510877e-001, 7.07195011e-002, 2.18797108e-002,
                  2.39280459e-001, 7.97667258e-001, 9.04050845e-001,
                  8.70564472e-001, 9.85277474e-001, 9.37414117e-200,
                  2.03896246e-001, 3.50493970e-001, 8.31993828e-001,
                  9.83971378e-001, 5.96992603e-001, 8.92232158e-001,
                  2.80851231e-001, 9.47324226e-001, 8.66293637e-001,
                  8.81295133e-001, 9.45908378e-001, 8.46658486e-001,
                  6.19767691e-001, 7.49522549e-001, 9.80327090e-001,
                  9.88546316e-001, 8.84031101e-001, 5.63877442e-001,
                  7.92633160e-001, 6.81020441e-001, 5.01605270e-001,
                  9.33430129e-001, 9.36099242e-001, 8.48409460e-001,
                  7.55103481e-001, 8.50806672e-001, 8.93576734e-001,
                  4.28571429e-001, 5.68623651e-001, 7.14589903e-001,
                  6.26107042e-001, 8.09981077e-001, 6.99214229e-001,
                  9.97959996e-001, 5.75331916e-001, 7.30257784e-001,
                  9.58790730e-001, 8.55208017e-002, 9.48941517e-001,
                  8.65697598e-001, 7.21974271e-001, 1.00000000e+000,
                  7.18166527e-001, 6.83568081e-001, 8.11936353e-001,
                  1.00000000e+000, 9.61385365e-001, 9.90541144e-001,
                  3.50758890e-001, 9.75599431e-001, 9.19880584e-001,
                  5.89994841e-001, 2.85715297e-001, 6.70866776e-001,
                  1.00000000e+000, 8.42200328e-001, 7.37511099e-001,
                  8.61580599e-001, 8.94830732e-001, 7.01128059e-001,
                  8.39940998e-001, 7.95225440e-001, 9.32664761e-001,
                  9.73898335e-001, 9.17767053e-001, 8.91759326e-001,
                  7.95967919e-001, 4.28574628e-001, 8.35151927e-001,
                  9.99743045e-001, 9.31092443e-001, 4.74416965e-002,
                  9.23317787e-002, 4.71309845e-001, 8.00232436e-001,
                  3.23599222e-001, 1.40316457e-001, 9.47314915e-003,
                  9.27785776e-001, 9.10166646e-001, 5.42163153e-001,
                  6.36804822e-001, 8.93922920e-001, 9.36443070e-001,
                  8.89758487e-001, 9.68676115e-001, 9.14599304e-001,
                  6.56402263e-001, 5.58160833e-002, 3.05696154e-001,
                  9.40985438e-001, 3.00085387e-001, 1.00000000e+000,
                  8.16099861e-001, 9.41663512e-001, 9.71549449e-001,
                  8.17213162e-001, 8.59593921e-001, 1.32822206e-067,
                  9.90519689e-001, 6.37789275e-001, 4.65003607e-002,
                  9.40821903e-001, 8.64879326e-001, 6.48867066e-001,
                  8.57064358e-001, 4.80814314e-002, 1.00000000e+000,
                  6.55727483e-001, 9.09334279e-001, 5.71775319e-001,
                  9.76315830e-001, 6.34754911e-001, 6.88890194e-001,
                  9.70758146e-001, 1.00000000e+000, 9.88155708e-001,
                  8.85938629e-001, 1.00000000e+000, 5.80785292e-001,
                  5.19619974e-001, 6.52424173e-001, 1.00000000e+000,
                  9.62115421e-001, 9.68608664e-001, 8.54007281e-001,
                  1.00000000e+000, 7.37855796e-001, 9.23901647e-001,
                  7.48352320e-001, 2.79893307e-001, 9.55241158e-001,
                  8.55172793e-001, 1.00000000e+000, 9.87496991e-001,
                  9.17409906e-001, 8.07808878e-001],
                 [9.91147379e-001, 9.71950756e-001, 9.66164853e-001,
                  9.90044290e-001, 8.99962002e-001, 9.94587492e-001,
                  8.66020842e-001, 9.85465521e-001, 8.04202840e-001,
                  8.24399544e-001, 9.83007729e-001, 9.70058188e-001,
                  1.00000000e+000, 9.90254104e-001, 9.91234813e-001,
                  5.31369822e-001, 2.24718517e-001, 8.90469000e-001,
                  8.77280044e-001, 1.00000000e+000, 9.98248406e-001,
                  9.64262814e-001, 9.91230697e-001, 2.87910465e-001,
                  9.96243598e-001, 9.57159268e-001, 8.43540065e-001,
                  1.00000000e+000, 9.43788897e-001, 9.85818169e-001,
                  6.61630686e-001, 9.58659755e-001, 9.89498599e-001,
                  9.56030570e-001, 8.88295817e-001, 8.76657314e-001,
                  9.95898473e-001, 9.24642411e-001, 9.51207291e-001,
                  9.98846374e-001, 8.32524309e-001, 9.35514570e-001,
                  9.97906933e-001, 9.42136798e-001, 9.96559331e-001,
                  9.78569836e-001, 9.22029550e-001, 9.75658656e-001,
                  9.58444027e-001, 7.26893631e-001, 9.81924614e-001,
                  9.55270543e-001, 9.26014646e-001, 7.52753488e-001,
                  8.96074270e-001, 1.00000000e+000, 1.00000000e+000,
                  9.55106964e-001, 8.24606882e-001, 7.85654073e-001,
                  9.82842642e-001, 9.99489133e-001, 9.51360285e-001,
                  6.44619682e-001, 9.66686257e-001, 8.46089129e-001,
                  1.00000000e+000, 1.00000000e+000, 9.92207465e-001,
                  9.09197734e-001, 4.75765006e-001, 2.30082747e-004,
                  1.00000000e+000, 8.86369167e-001, 9.76311590e-001,
                  8.99593976e-001, 9.37533944e-001, 8.63609870e-001,
                  9.43352461e-001, 9.91860418e-001, 9.96610396e-001,
                  2.04636538e-001, 9.39350163e-001, 7.07500520e-001,
                  5.09314144e-001, 8.55112711e-001, 1.00000000e+000,
                  9.92517100e-001, 8.84447208e-001, 9.97166101e-001,
                  3.03456180e-005, 5.40383239e-001, 9.71030311e-001,
                  4.15600517e-002, 9.72643552e-001, 1.00000000e+000,
                  8.75821896e-001, 8.79409076e-001, 9.87258016e-001,
                  1.00000000e+000, 9.15935525e-001, 9.23668346e-001,
                  9.92023976e-001, 5.93212910e-001, 9.95807177e-001,
                  8.42293888e-001, 9.65433769e-001, 9.95176039e-001,
                  8.65023384e-001, 9.04339253e-001, 9.03248686e-001,
                  9.96433427e-001, 9.89774865e-001, 7.90177353e-001,
                  9.49047386e-001, 9.21470330e-001, 2.09843101e-001,
                  9.76699957e-001, 9.13804468e-001, 9.53999714e-001,
                  9.70586020e-001, 8.66469430e-001, 9.68688535e-001,
                  9.97454638e-001, 1.99703148e-001, 6.58721857e-001,
                  9.88596768e-001, 8.62785846e-001, 9.95191227e-001,
                  9.84517299e-001, 9.66423119e-001, 9.44480097e-001,
                  9.50341683e-001, 6.97671354e-001, 9.89384484e-001,
                  8.99064119e-001, 7.83812466e-001, 2.83738349e-002,
                  9.21598247e-001, 9.84759816e-001, 8.72653996e-001,
                  9.59305279e-001, 9.74310428e-001, 9.36729554e-001,
                  9.53490892e-001, 9.59016933e-001, 9.29383300e-001,
                  9.56924034e-001, 2.12905791e-001, 3.11554859e-001,
                  7.67775706e-001, 9.89225339e-001, 9.00663911e-001,
                  9.85652947e-001, 9.67385744e-001, 9.82055763e-001,
                  9.90816449e-001, 7.34307920e-001, 5.89091994e-001,
                  9.70713419e-001, 5.90632197e-001, 7.67521255e-001,
                  7.91860619e-001, 9.34818881e-001, 6.87735071e-001,
                  9.62728070e-001, 6.09425808e-001, 8.08485392e-001,
                  9.16510215e-002, 2.09072842e-001, 9.53930596e-001,
                  6.21810775e-001, 9.87612685e-001, 9.99011694e-001,
                  9.43293593e-001, 6.24050225e-001, 7.93338055e-001,
                  1.00000000e+000, 8.10497021e-001, 9.64038648e-001,
                  9.71492664e-001, 8.88371723e-001, 9.01374872e-001,
                  9.95021276e-001, 9.61329989e-001, 5.38656618e-001,
                  7.04863056e-001, 9.73119470e-001, 1.00000000e+000,
                  9.95106717e-001, 9.75706315e-001, 1.00000000e+000,
                  4.83874150e-001, 8.15151985e-001, 9.66772030e-001,
                  9.84630615e-001, 5.80503503e-001, 9.97486296e-001,
                  9.52368139e-001, 9.45937523e-001, 9.87133657e-001,
                  1.44676916e-001, 9.29609197e-001, 9.77275547e-001,
                  2.71011611e-001, 9.67923108e-001, 9.29981363e-001,
                  8.88573398e-001, 9.94708921e-001, 9.49523011e-001,
                  9.89263407e-001, 9.82159915e-001, 9.21548082e-001,
                  6.11092334e-001, 9.97523067e-001, 8.84511095e-001,
                  9.70288964e-001, 9.62247950e-001, 8.13831477e-001,
                  9.79740680e-001, 9.60187791e-001, 7.39476447e-001,
                  8.16858344e-001, 9.62282760e-001, 9.64015648e-001,
                  9.26618007e-001, 8.03640939e-001, 9.89798229e-001,
                  9.20630601e-001, 9.73831343e-001, 9.39612786e-001,
                  9.89602013e-001, 8.31983694e-001, 9.98690219e-001,
                  9.77639073e-001, 1.00000000e+000, 9.80649004e-001,
                  7.69267181e-001, 8.92907972e-001, 9.94293952e-001,
                  9.01223037e-001, 9.72418989e-001, 9.81164809e-001,
                  9.03453967e-001, 9.96054730e-001, 5.59525351e-001,
                  9.95348273e-001, 7.98633617e-001, 8.77325269e-001,
                  9.83331317e-001, 3.90902716e-001, 9.79332640e-001,
                  9.74127534e-001, 4.50074264e-001, 8.38049960e-001,
                  7.68579732e-002, 9.66325610e-001, 9.93313629e-001,
                  6.47304242e-001, 8.69869120e-001, 8.37211897e-001,
                  9.83199430e-001, 4.37429024e-001, 9.37301515e-001,
                  1.60795702e-002, 1.80639407e-001, 4.31620574e-001,
                  9.76523772e-001, 4.30740143e-001, 9.06878162e-001,
                  5.74473577e-001, 9.73795204e-001, 1.00000000e+000,
                  6.50207891e-001, 9.93753202e-001, 9.52524180e-001,
                  9.92896342e-001, 7.31238657e-001, 9.49123785e-001,
                  6.71207423e-001, 9.77894909e-001, 3.74868040e-001,
                  9.44448423e-001, 9.66477679e-001, 9.87138720e-001,
                  9.09704105e-001, 9.83395464e-001, 8.01274007e-001,
                  7.89448924e-001, 8.21409164e-001, 9.42463389e-001,
                  9.79780242e-001, 7.49125807e-001, 9.92424146e-001,
                  6.99023733e-001, 9.09972014e-001, 9.12205907e-001,
                  8.90706226e-001, 5.40540598e-001, 9.92769685e-001,
                  8.13835268e-001, 9.99086032e-001, 9.95546042e-001,
                  1.00000000e+000, 9.38014644e-001, 1.90608413e-001,
                  1.00000000e+000, 9.55855640e-001, 8.15048232e-001,
                  9.37276439e-001, 9.84767085e-001, 7.58388823e-001,
                  9.90774947e-001, 9.94336592e-001, 6.80002580e-001,
                  6.55607632e-001, 8.79611368e-001, 9.92928091e-001,
                  9.32765535e-001, 9.74458631e-001, 9.97860374e-001,
                  8.51225575e-001, 9.37751930e-001, 9.10183081e-001,
                  9.17020768e-001, 1.00000000e+000, 9.86404911e-001,
                  8.62356279e-001, 9.60048557e-001, 5.31342359e-001,
                  8.12732517e-001, 9.92717382e-001, 9.97553965e-001,
                  3.01832200e-001, 9.96128596e-001, 8.77590631e-001,
                  1.00000000e+000, 9.86484943e-001, 7.48789338e-001,
                  7.60629596e-001, 9.02519643e-001, 1.00000000e+000,
                  8.76007973e-001, 8.65114983e-001, 9.96436417e-001,
                  9.46368712e-001, 9.62792077e-001, 9.52414419e-001,
                  8.47955480e-001, 9.91874114e-001, 9.86230256e-001,
                  9.94163413e-001, 9.99313914e-001, 8.61302289e-001,
                  9.14317420e-001, 9.50097933e-001, 7.76309186e-001,
                  9.76887202e-001, 9.57457100e-001, 9.54560375e-001,
                  9.68189396e-001, 9.58733692e-001, 9.92666973e-001,
                  6.12553202e-001, 9.88046020e-001, 9.67017050e-001,
                  9.38095092e-001, 9.44329823e-001, 9.48251262e-001,
                  9.12011432e-001, 8.05815147e-001, 3.01454697e-001,
                  9.88776102e-001, 9.32445038e-001, 8.25879760e-001,
                  5.56368140e-001, 1.00000000e+000, 9.87556731e-001,
                  9.18449703e-001, 8.75782460e-001, 9.97836835e-001,
                  8.99619522e-001, 9.54744730e-001, 9.99854772e-001,
                  9.98885645e-001, 7.01280823e-001, 9.90628011e-001,
                  9.14458462e-001, 9.63638478e-001, 9.37876978e-001,
                  9.77900327e-001, 5.22784738e-001, 4.03676032e-001,
                  9.37313500e-001, 8.97972642e-001, 9.99783799e-001,
                  8.86523265e-001, 8.74092337e-001, 1.00000000e+000,
                  7.15666285e-001, 4.36484787e-001, 9.47444772e-001,
                  9.86001975e-001, 9.21410448e-001, 9.59581517e-001,
                  9.41665390e-001, 8.65504066e-001, 9.28833560e-001,
                  9.71127158e-001, 8.49226397e-001, 9.85351190e-001,
                  9.59521856e-001, 9.44883522e-001, 9.62561802e-001,
                  8.91407891e-001, 9.98951233e-001, 9.91725091e-001,
                  9.41195576e-001, 9.54785312e-001, 9.89622944e-001,
                  9.72211466e-001, 7.68030455e-001, 9.18510998e-001,
                  9.77385875e-001, 9.34273126e-001, 8.13575755e-001,
                  1.00000000e+000, 9.99165677e-001, 9.39979846e-001,
                  9.04483454e-001, 9.12474278e-001, 9.64830930e-001,
                  9.82811048e-001, 9.81284951e-001, 7.66248589e-001,
                  1.00000000e+000, 8.33995819e-001, 9.77581930e-001,
                  6.43567368e-001, 9.96575975e-001, 8.98904567e-001,
                  5.74750264e-001, 3.17044175e-001, 1.00000000e+000,
                  8.95102867e-001, 7.81600476e-001, 1.00000000e+000,
                  9.19912251e-001, 9.96642046e-001, 7.92473741e-001,
                  9.82915546e-001, 9.95027400e-001, 9.96178055e-001,
                  8.56028297e-001, 9.47404325e-001, 9.36733098e-001,
                  9.63971987e-001, 9.96684608e-001, 8.90387146e-001,
                  7.34300724e-002, 9.69701948e-001, 9.44124130e-001,
                  9.83594936e-001, 9.25784233e-001, 5.80448001e-001,
                  1.00000000e+000, 9.92149129e-001, 9.40362213e-001,
                  1.00000000e+000, 7.80406441e-001, 8.81126100e-001,
                  6.64381931e-001, 9.86171098e-001, 4.61282937e-001,
                  1.00000000e+000, 7.58499002e-001, 8.83415421e-001,
                  9.64025159e-001, 9.60763067e-001, 9.48179446e-001,
                  5.90266116e-001, 9.24629732e-001, 2.00058914e-001,
                  6.05169585e-001, 8.18267303e-001, 9.97805436e-001,
                  1.00000000e+000, 7.73787636e-001, 1.00000000e+000,
                  9.83944219e-001, 1.20935597e-030, 8.86723710e-001,
                  8.48147942e-001, 9.59844921e-001, 9.66619335e-001,
                  9.33360236e-001, 9.39173966e-001, 9.64370008e-001,
                  9.71246723e-001, 9.93454895e-001]])
        • step_size
          (chain, draw)
          float64
          0.5415 0.5415 ... 0.594 0.594
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        • max_energy_error
          (chain, draw)
          float64
          -0.149 2.22 ... 0.09263 -0.2259
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                   4.98040972e-01,  4.02776412e+00, -3.39673281e-01,
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                  -5.08268391e-01,  7.45951887e-01, -2.95089806e-01,
                  -2.21708949e-01,  7.05258237e-01, -6.39449462e-01,
                   8.28030896e-01,  1.74208446e+03,  2.87961006e+00,
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                  -1.75408834e-01,  9.26871157e-02,  7.78499489e-02,
                   8.20325140e-02,  1.09039753e-01, -1.99338337e-01,
                   2.33428202e+00, -1.15071017e-01, -2.69497332e-01,
                   1.10467892e-01,  1.46006785e-01,  1.32930000e-01,
                   1.31830682e-01,  3.16101472e-01,  5.00470178e+00,
                  -3.41020535e-01, -3.06145546e-01,  6.83923151e-01,
                   1.14220906e+01, -2.66391502e-01, -3.77823075e-01,
                  -3.73029410e-01,  3.31440380e-01, -4.80878279e-01,
                   1.79627602e-01,  2.99343576e-01, -3.20955745e-01,
                  -2.11263382e-01,  1.01154867e+00, -2.90199553e-01,
                   1.36103559e-01, -1.91689867e-01,  5.20064128e-01,
                  -1.79664991e-01,  1.07882257e+01,  4.58574278e+01,
                   1.80381906e-01,  2.23343865e-01, -3.72677286e-01,
                   2.58994449e-01,  4.05874751e-01, -1.37774088e-01,
                   7.28032205e-01,  7.17636526e+00,  1.45501040e-01,
                  -1.69225619e-01,  1.47533611e-01,  1.76079043e-01,
                   1.60345771e-01,  2.55957854e-01, -2.68604960e-01,
                   6.36591410e-02,  2.87081659e-01, -1.08966167e-01,
                   9.61128383e-02,  1.36872190e-01,  1.23013604e-01,
                   7.50570921e-01, -2.43563140e-01,  4.51026693e-02,
                   1.29231657e-01, -1.37736002e-01, -1.44702278e-01,
                  -4.85750501e-01,  3.91839192e-01,  3.20403337e-01,
                  -7.95553123e-02,  1.79980691e-01,  4.44031299e-01,
                  -2.55707917e-01, -1.02071175e-01,  8.18704885e-02,
                  -5.67237728e-01,  2.50222433e-01, -3.83524211e-01,
                  -2.48871791e-01,  5.56381462e-02,  3.59204501e-01,
                  -1.42082094e-01,  4.78843019e-01, -1.40871993e-01,
                   1.66546635e+00, -2.61810891e-01, -5.19252400e-01,
                   1.53687134e+01,  3.72049407e+00, -1.22635133e+00,
                   1.79981186e-01,  1.96649255e+00, -7.70618309e-02,
                   2.16772080e-01, -6.36733593e-02,  3.72045282e-01,
                  -1.09774573e-01, -1.35848603e-01, -1.89825359e-01,
                   3.03534925e-01,  1.55306550e-01,  1.47716265e-01,
                   1.18696244e-01, -2.85207166e-01,  4.19819584e-01,
                   5.18986892e+00,  1.00885783e-01, -2.04425122e-01,
                  -1.40849261e-01,  1.79701174e-01,  1.07057396e+00,
                  -4.11514293e-01, -1.26332174e-01, -8.15107271e-01,
                  -2.77782962e-01,  3.25116993e-01,  1.20757101e+00,
                   1.66572145e+00, -4.32564272e-01,  1.25543147e+00,
                  -2.43918883e-01,  5.09511785e-01,  5.96079844e-01,
                  -1.93127301e-01, -1.37330386e-01, -2.52257750e-01,
                   1.42156714e+00,  1.56195761e-01,  8.36186033e+00,
                   9.15127220e-01, -5.65338705e-01, -7.87366471e-01,
                  -3.90881221e-01,  5.18319151e-01, -3.92801976e-01,
                  -3.37473071e-01,  6.88874648e+01,  2.24396299e-01,
                   4.08363766e+00, -8.83842396e-02,  1.67991437e-01,
                   1.68452977e-01, -2.73194417e-01,  1.09057868e-01,
                   9.26317764e-02, -2.25943052e-01]])
        • tree_size
          (chain, draw)
          float64
          7.0 7.0 7.0 7.0 ... 7.0 7.0 7.0 7.0
          array([[ 7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  5.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   3.,  7.,  7.,  3.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  1.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,
                   3.,  7.,  7.,  7.,  3.,  7.,  7.,  6.,  7.,  7.,  3.,  7.,  7.,
                   3.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  3.,  3.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,  1.,
                   7.,  7.,  7.,  3.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,
                   7.,  3.,  7.,  7.,  7.,  7.,  3.,  7.,  3.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  3.,  3.,  3.,  3.,  7.,  7.,  7.,
                   7.,  3.,  7.,  7.,  1.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  3.,  1.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  3.,  1.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,  3.,  7.,
                   7.,  7.,  7.,  7.,  7.,  1.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,  3.,  7.,  7.,  7.,  3.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  3.,  3.,  7.,
                   7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,  1.,  3.,
                  15.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  3.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,
                   3.,  7.,  7.,  7.,  7.,  7.,  1.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,  3.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.],
                 [ 7.,  7., 15.,  7., 15.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7., 15.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,
                   7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  3.,  7.,  7., 15.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,  7., 15.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7., 15.,  7., 15.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7., 15.,  7.,  7.,  7.,
                   7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7., 15., 15.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                  15.,  7., 15.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7., 15.,
                   7.,  7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   3.,  7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7., 15.,  7.,  7.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7.,  3.,  7.,  1.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.]])
        • energy_error
          (chain, draw)
          float64
          -0.1261 0.5558 ... -0.05267
          array([[-1.26073671e-01,  5.55780576e-01, -7.27591431e-02,
                  -2.42733853e-01,  2.69058870e-01, -3.10309436e-01,
                  -2.28594235e-01,  2.88516746e-01, -1.34207283e-01,
                   7.56506289e-02,  1.41018753e-02, -8.55723457e-02,
                   8.71437172e-02, -8.31500456e-03,  2.72671949e-01,
                  -3.72090705e-01,  5.62033095e-04, -9.12109435e-02,
                  -1.53104812e-01,  1.07862839e-01,  2.65541267e-01,
                  -6.42682763e-01,  0.00000000e+00,  2.52295139e-01,
                  -1.10616634e-01,  2.12548259e-01, -1.03926361e-02,
                  -5.04986109e-01,  4.13848460e-01, -7.97687495e-01,
                   3.54780172e-01, -1.12787935e-01,  1.66906991e-01,
                   2.45362775e-01, -8.93673703e-02,  2.31968101e-01,
                   0.00000000e+00, -8.18909645e-01,  4.89476357e-01,
                  -2.91927233e-02,  6.61811222e-01,  4.04787278e-01,
                  -1.36523121e-01, -2.35368597e-02,  1.43463992e+00,
                   4.27003572e-02, -8.29382867e-01,  1.40416069e-01,
                   9.54788225e-02,  7.24462871e-02, -1.24093852e-01,
                   1.64837114e-03, -4.93491567e-01, -3.91735572e-01,
                   4.62170795e-01, -5.74977164e-01,  1.40822480e+00,
                  -1.95469025e-01,  5.54528049e-02,  2.63869249e-01,
                  -5.46685951e-01, -1.99327188e-01, -6.49196643e-02,
                   1.50740585e+00,  6.24992410e-01,  1.82133321e-01,
                  -6.62691220e-02,  1.91084119e-02,  1.39688603e-01,
                  -2.74597344e-01, -1.03443030e-01,  5.52638788e-01,
                  -7.64666643e-01, -4.72640496e-01, -5.16348796e-01,
                   2.48894407e-01, -1.04486589e+00,  2.61986693e-01,
                   1.03015516e-01,  1.11157560e+00,  1.64573671e-01,
                   0.00000000e+00,  5.72809685e-01, -7.39786129e-01,
                   1.49448987e-01,  3.96423978e+00, -1.95557069e-01,
                  -1.30865850e-01, -7.96888433e-01, -5.66029114e-02,
                   5.00899554e-01, -3.01556925e-01, -7.51908574e-02,
                   3.44335390e-02,  2.95193166e-01,  0.00000000e+00,
                  -1.67040389e+00, -1.89375136e-01, -6.69257331e-02,
                  -5.71472468e-01, -1.01412010e-01, -4.74222427e-02,
                   6.65210297e-01,  4.81809560e-01, -6.45115769e-01,
                  -4.98056614e-02,  8.04357034e-01, -1.79670162e-02,
                  -3.16063846e-01,  3.17368085e-01,  4.62968258e-01,
                   9.53648784e-02,  0.00000000e+00,  1.62234592e-01,
                  -9.11974481e-02, -7.09183807e-02, -4.63608619e-01,
                  -5.08268391e-01,  3.79762165e-01,  2.35583734e-01,
                  -1.35074674e-01,  5.02728294e-02,  1.27296760e-01,
                   1.55638078e-01,  1.29441092e-01, -3.17342085e-01,
                   4.50042704e-01, -1.47885639e+00,  1.58885491e-01,
                  -3.22279272e-02, -9.46533193e-01,  3.06130021e-01,
                   1.12662757e-01,  0.00000000e+00,  2.23305166e-01,
                   3.29358548e-01, -3.27353951e-02, -2.07844522e-01,
                   1.70926031e-01, -3.97526443e-02,  2.10113673e-01,
                  -3.18129947e-01,  2.45979519e-01, -3.16914460e-01,
                  -1.34170878e-02, -5.60473748e-01,  6.52740607e-01,
                   8.98127201e-02, -2.83061481e-01,  3.28089369e-02,
                   1.58036364e+00, -1.47108682e-01, -4.05742820e-01,
                   6.93008169e-01,  1.84777480e-01,  0.00000000e+00,
                   2.39780962e-03,  2.29156188e-01,  6.08625233e-02,
                  -5.06520435e-01, -1.78900224e-02,  1.49135233e-01,
                   4.83391765e-01, -6.56196928e-01,  3.13548792e-02,
                   5.66260436e-01,  5.55733196e-01, -2.77489363e-02,
                   9.10028126e-01,  1.37733199e-01,  6.79112866e-01,
                  -9.24288392e-01,  5.21517674e-02,  2.25598651e-01,
                  -9.27740875e-01,  0.00000000e+00, -1.80135496e-02,
                   2.79401240e-01, -4.97018126e-02, -1.27277580e-01,
                   6.64363613e-02, -1.03533066e-01,  1.72033431e-01,
                  -2.46607279e-01,  1.13620069e-01,  4.08848761e-01,
                  -1.74226499e-01,  1.04834108e-01, -1.69977861e-01,
                  -2.85688974e-01, -1.78935065e-01,  3.01749981e-01,
                   7.37011214e-01, -2.04104061e-01, -1.80767132e-01,
                  -1.42189086e-02,  1.00102585e-01,  1.82258868e-02,
                   1.82522066e-01,  2.33312676e-01, -1.14414675e+00,
                   1.18106320e-01,  0.00000000e+00, -2.59611150e-01,
                  -1.12621457e-01, -4.06804553e-02,  9.57649002e-02,
                   2.72782296e-02, -6.23834342e-02,  0.00000000e+00,
                   1.82267424e-01,  1.70987404e-01,  0.00000000e+00,
                   3.55827242e-01, -7.65995759e-01,  7.77433489e-02,
                   7.50343565e-01, -1.03408389e+00,  1.82977832e-01,
                  -2.28379635e-01,  3.26791036e-01, -3.05040041e-01,
                  -1.35141652e-02,  2.49914567e-01, -4.80919275e-01,
                   5.62281466e-01,  1.59071643e-01,  2.36130934e-01,
                   2.05860564e-01, -8.69692271e-01, -2.01723119e-01,
                  -2.93409508e-01, -2.12195478e-02, -4.52063253e-01,
                  -1.12095243e-01,  4.38773330e-04,  1.25615569e-02,
                   3.64299410e-02, -4.61375526e-02, -4.94261432e-01,
                   2.88048115e-01,  1.87130219e-01,  7.78605244e-03,
                   3.31375905e-01, -3.35956569e-01, -3.07223577e-01,
                  -9.14639855e-02, -7.69447548e-03,  4.84629780e-01,
                   0.00000000e+00,  1.05387938e-01, -1.75258989e-01,
                   7.44165307e-02, -3.42050471e-02,  1.96873259e-01,
                   4.64836213e-01,  2.72885885e-02,  1.66827008e-01,
                  -2.68812261e-01, -3.16695338e-02,  1.50610694e-01,
                   1.47372219e-01, -1.65573668e-01, -2.21925605e-01,
                   2.60113836e-02,  2.57389333e-01,  5.50416990e-01,
                  -1.87877422e-01, -2.08650276e-01,  1.33193376e-01,
                  -8.76507356e-02,  1.50573827e+00, -1.31612922e+00,
                   1.17930702e-02,  5.62168525e-02, -1.63709187e-03,
                  -8.50364270e-01,  0.00000000e+00, -1.43382513e-02,
                   7.89808871e-02,  9.40740090e-02,  1.56137391e-01,
                  -8.64664497e-02,  2.77776345e-01, -4.65959296e-01,
                  -4.40614662e-01,  4.32314205e-01, -6.76974063e-01,
                  -9.62671199e-02, -2.06055034e-01, -1.14494587e-01,
                  -3.18475481e-02,  9.49747850e-01, -4.68858902e-01,
                  -6.10585233e-02, -8.18488916e-02,  8.57446542e-01,
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        • diverging
          (chain, draw)
          bool
          False False False ... False False
          array([[False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False,  True, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False,  True, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False,  True,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False],
                 [False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False]])
        • depth
          (chain, draw)
          int64
          3 3 3 3 3 3 3 3 ... 3 3 3 3 3 3 3 3
          array([[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3,
                  3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 2, 3, 3, 3, 3, 3,
                  3, 1, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2,
                  3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 3, 3, 1, 3, 3, 3, 2, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 3, 3, 3, 2,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 1, 3, 3, 3,
                  2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3,
                  3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 2, 2, 3, 3,
                  3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 1, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3,
                  3, 3, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 1,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3,
                  3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3],
                 [3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3,
                  3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2,
                  3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 4, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4,
                  3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3,
                  3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3,
                  3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 3, 3, 2, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3]])
        • lp
          (chain, draw)
          float64
          -45.78 -49.19 ... -45.28 -43.83
          array([[-45.78048101, -49.18878918, -47.81124046, -45.88878259,
                  -48.31089296, -45.14855162, -44.49296796, -47.06173477,
                  -46.00333193, -46.74945341, -45.31134603, -44.57091151,
                  -45.21360856, -45.08678676, -48.93014192, -44.3319601 ,
                  -44.10683405, -43.35268252, -43.03524428, -43.93322003,
                  -46.08079228, -45.6846219 , -45.6846219 , -46.15356626,
                  -46.04213007, -49.38770053, -48.34053206, -43.80699611,
                  -45.51102992, -45.96717108, -48.69233529, -46.14925774,
                  -44.29064411, -46.93019508, -46.63176458, -45.86788665,
                  -45.86788665, -43.88184986, -47.85223431, -46.89128814,
                  -45.37435027, -49.80568336, -47.92276381, -46.58699925,
                  -46.93876301, -49.68452069, -44.46531184, -44.22245826,
                  -46.62746534, -45.97081079, -44.73635903, -44.82874639,
                  -50.01955523, -44.55905088, -47.35901965, -47.73677562,
                  -50.42675194, -48.81429299, -47.71982842, -51.4284502 ,
                  -47.47346232, -46.0599324 , -44.66857095, -42.01852763,
                  -45.68232031, -46.65687534, -45.86968195, -47.0690995 ,
                  -48.19324334, -46.3852222 , -44.90130478, -50.16581678,
                  -45.36505614, -44.05814881, -42.63294644, -42.26222755,
                  -44.621209  , -44.01706864, -49.5334657 , -51.81656903,
                  -48.8597275 , -48.8597275 , -51.53180885, -47.33636019,
                  -44.96535688, -51.38637552, -47.45798166, -46.01224865,
                  -44.86837616, -44.42754385, -46.86798685, -44.3426595 ,
                  -44.05714857, -43.53446044, -45.43752874, -45.43752874,
                  -45.52642893, -47.19017679, -45.83775196, -44.18596385,
                  -42.8669047 , -42.28571587, -47.96598513, -52.21374203,
                  -45.0182377 , -42.05238676, -48.19013005, -48.54712061,
                  -45.53565943, -47.38524796, -49.99698174, -49.38402006,
                  -49.38402006, -50.29769779, -49.58451027, -48.9940765 ,
                  -47.40922232, -42.6843339 , -45.19096453, -46.3147075 ,
                  -43.65597466, -44.35146644, -44.52390399, -46.17249626,
                  -46.99344625, -46.80208718, -48.65544225, -48.21334325,
                  -47.32004813, -47.21866465, -45.32097994, -44.32968141,
                  -46.91120509, -46.91120509, -48.43712029, -48.16994442,
                  -48.90512804, -48.9750313 , -51.97941409, -52.66710777,
                  -56.32411594, -52.43433435, -50.34598173, -47.8481962 ,
                  -48.07973757, -41.93572432, -48.05793509, -47.15547856,
                  -44.74877076, -44.89475534, -44.80333795, -43.51894208,
                  -41.89061071, -43.65392569, -43.37718169, -43.37718169,
                  -43.2104204 , -45.13167633, -46.98790503, -45.22230073,
                  -43.84019779, -45.00268433, -46.00206013, -43.9482027 ,
                  -43.53136853, -45.46703817, -50.09255333, -49.07799469,
                  -49.86766183, -51.08149183, -46.11713442, -45.58760963,
                  -46.73611561, -48.63966549, -46.68674661, -46.68674661,
                  -45.52232661, -44.38351214, -44.23031392, -42.12893314,
                  -42.47836156, -44.45234942, -46.43426052, -44.97640048,
                  -45.58007924, -46.85188349, -46.72341757, -47.7518406 ,
                  -45.54010468, -45.64070562, -42.66211512, -45.26554496,
                  -47.51112123, -46.06975612, -43.80513371, -43.60156368,
                  -45.03688531, -44.88897982, -47.19986063, -48.80261935,
                  -48.9907256 , -54.26084662, -54.26084662, -52.39727346,
                  -48.86544723, -46.67034391, -47.36369937, -47.19084335,
                  -45.12933197, -45.12933197, -44.66262481, -46.16517094,
                  -46.16517094, -52.38813091, -43.07196695, -43.2195468 ,
                  -51.96978017, -45.42799992, -45.99615639, -43.55327637,
                  -44.50695961, -45.6998766 , -45.70502721, -47.99935484,
                  -43.13146399, -43.57610803, -45.81830378, -50.3246228 ,
                  -49.3761429 , -44.63956128, -44.847414  , -44.39839394,
                  -44.82008212, -43.89094371, -43.3909851 , -43.38065627,
                  -43.7254173 , -46.55605626, -44.54607308, -43.87475625,
                  -44.46730896, -45.1254539 , -45.44825418, -48.34883785,
                  -47.96583867, -45.31978276, -44.67587553, -45.44690251,
                  -46.36533237, -46.36533237, -47.7205891 , -46.99252322,
                  -47.61037517, -47.51413814, -49.47857824, -42.99020352,
                  -43.70212084, -46.88856401, -43.88205174, -44.25054476,
                  -45.0344157 , -47.37595235, -46.81145515, -45.20292072,
                  -44.17101765, -43.80468746, -50.98766494, -48.90351247,
                  -47.03958194, -47.9377543 , -47.33091331, -52.16843057,
                  -46.18186146, -46.3061205 , -46.92302927, -45.92532396,
                  -47.24810558, -47.24810558, -47.78016312, -48.54230889,
                  -49.06151437, -50.16738166, -51.91271646, -53.04146531,
                  -50.02860505, -45.57792072, -49.8402585 , -46.55624754,
                  -46.63781942, -43.97856323, -43.26051807, -43.51553281,
                  -47.47969118, -43.62766387, -43.32832777, -44.27385417,
                  -50.04026684, -50.83512193, -46.39175304, -48.02551726,
                  -45.97132734, -44.62326489, -43.02075358, -43.98890991,
                  -43.98890991, -43.21772264, -44.78356048, -44.12231097,
                  -51.1896688 , -51.6929149 , -51.94097296, -46.79485256,
                  -47.58220479, -47.00889942, -44.99743198, -46.81183039,
                  -47.89345798, -44.53254874, -44.53254874, -45.29515429,
                  -45.29515429, -45.35516839, -48.74100196, -45.97289177,
                  -44.62343347, -47.93487626, -47.0310884 , -47.29981185,
                  -47.13848913, -46.91289295, -43.83363984, -43.29437474,
                  -47.53067682, -48.91013391, -44.76560913, -43.80501702,
                  -44.65727243, -46.34867805, -48.91944387, -45.42252701,
                  -43.62965689, -45.96222457, -46.89336622, -46.08638633,
                  -51.21905709, -50.62329425, -54.13463139, -47.97350676,
                  -42.84671559, -50.928357  , -48.69214433, -49.47091335,
                  -47.3377065 , -49.58787899, -47.60402705, -52.56415554,
                  -52.56415554, -46.63174391, -46.84335105, -45.75900974,
                  -45.91413216, -46.651234  , -46.651234  , -49.84704697,
                  -44.53404821, -44.13203948, -43.69285268, -45.89734544,
                  -46.21609033, -45.98898381, -46.9970694 , -49.24739837,
                  -50.28043729, -49.10806334, -50.41178617, -45.73251499,
                  -46.09281649, -44.52925914, -44.13666276, -44.29012323,
                  -43.78974097, -45.35667529, -48.44378554, -49.74685978,
                  -47.0403272 , -45.34390997, -50.75265946, -49.5701038 ,
                  -50.89077564, -52.50178734, -44.82294086, -45.81617068,
                  -46.85299469, -42.35464476, -43.8227742 , -45.9386359 ,
                  -46.95672169, -49.52222389, -47.89112801, -47.21330091,
                  -47.21330091, -46.61604754, -47.23720398, -50.25577858,
                  -47.20127448, -44.55965628, -45.08448349, -49.01631313,
                  -46.87294711, -44.81120796, -43.8286461 , -48.2208947 ,
                  -47.4438895 , -48.18728969, -50.76498659, -44.94063704,
                  -50.68973422, -48.23292987, -47.11553166, -51.09615344,
                  -50.18621853, -46.09572695, -42.81722982, -45.84979875,
                  -43.53758146, -42.86040454, -45.36400087, -44.96261261,
                  -45.18434439, -46.69045773, -46.51233255, -45.48438348,
                  -43.28125786, -42.21138617, -42.21138617, -43.76358652,
                  -48.75561113, -47.58626301, -42.31839949, -44.53782023,
                  -44.53782023, -44.96273809, -45.25575418, -50.20937923,
                  -44.40153283, -42.275109  , -43.08078662, -43.85484947,
                  -43.0944096 , -43.25267066, -43.64940501, -43.64940501,
                  -46.48272131, -46.06836256, -46.06836256, -43.40173601,
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      • created_at :
        2020-06-10T18:19:23.335024
        arviz_version :
        0.8.3
        inference_library :
        pymc3
        inference_library_version :
        3.8

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
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        • draw: 500
        • school: 8
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                   1.09979417,  0.40300613, -0.99749685,  1.75980059,  2.72177195,
                   2.58293073,  1.05452379,  0.26683768, -0.08899415,  1.8233168 ,
                   1.25087499,  0.51544631,  1.71713821, -0.07991098,  1.04087024,
                   1.92818799, -0.35251242,  2.77931855,  1.26470085,  1.39402269,
                   1.69576834,  2.69417672,  1.35947815,  1.28346478,  0.97858565,
                   2.01678674,  2.77387222,  1.22566557,  2.8065254 ,  2.39601751,
                   2.79108204,  3.22977667,  2.34095033,  1.21336144,  2.65564027,
                   0.85456707,  2.84012414,  1.32798643,  0.71154812,  3.49958034,
                  -0.45660104,  1.81603681,  1.96863298,  3.10477242,  0.02468627,
                   0.6817256 ,  3.54044187,  3.26327222,  1.65833051,  1.42266403,
                   1.18580882,  3.200757  ,  2.84417962,  2.09119768,  0.01526257,
                   1.78042628,  1.67860247,  0.53106916,  2.20371117,  2.16164611,
                   0.75287014,  1.77576973,  2.20152037,  3.19102252,  2.9998979 ]])
        • tau
          (chain, draw)
          float64
          5.507 8.185 0.4056 ... 24.31 20.08
          array([[5.50686275e+00, 8.18498929e+00, 4.05560437e-01, 1.30457567e+01,
                  1.64504830e+01, 2.69962919e+00, 2.01269022e+01, 8.99097276e-01,
                  1.87625645e+00, 4.40620548e+00, 8.75700183e+00, 2.43239497e+00,
                  1.44189180e+00, 1.76826038e+01, 6.59324864e-02, 1.38897985e+01,
                  2.96988714e+00, 8.59686709e-01, 4.54883689e+00, 3.08040285e+00,
                  8.18501327e+00, 9.65243249e+00, 7.83833691e+00, 3.75150607e+00,
                  3.98325370e+00, 7.42502229e+00, 9.52694584e-01, 1.22156659e+00,
                  1.09420480e+00, 3.72055864e+01, 3.73287963e-01, 8.53960826e+00,
                  9.45041492e+01, 1.75767299e+00, 8.06157503e+00, 6.14265162e+00,
                  7.02672777e+00, 6.96026860e+00, 2.87512835e+01, 2.05550166e+01,
                  3.77273632e+00, 8.79722240e+00, 1.69188711e+00, 1.25566346e+00,
                  8.17259137e+00, 1.82778393e+01, 3.99297764e+00, 3.80219282e+00,
                  2.36415060e+00, 1.83460476e+01, 4.99244772e+01, 1.40951424e+01,
                  1.33904739e+01, 4.73324937e+00, 8.23979948e-01, 1.85632561e+00,
                  1.06323880e+00, 3.06079899e+00, 2.50876515e+01, 1.70800873e+01,
                  5.94768225e+01, 3.88743982e-01, 7.73087020e+02, 9.58932810e+00,
                  2.59773692e+00, 2.56898968e+00, 4.65870778e+00, 3.57595288e+00,
                  1.03628487e+00, 9.99755332e+00, 2.90034686e+00, 1.39189281e+01,
                  1.22445884e+01, 1.56928895e+00, 1.75223948e+00, 4.44499093e+00,
                  1.69158665e+01, 1.03938259e+01, 5.45555640e+00, 5.98212863e+00,
                  4.56998241e+00, 3.40803695e+00, 1.79360042e+01, 5.68076540e+00,
                  8.56050879e+00, 1.80674094e+00, 2.47088071e+00, 1.23765481e+01,
                  4.28460931e-01, 1.05729781e+01, 3.78579568e+00, 1.67395498e+00,
                  1.26755323e+01, 1.18075397e+01, 9.08358961e+00, 1.12642945e+00,
                  7.25749272e+00, 3.48764152e+00, 4.00327093e+00, 9.72734690e+00,
                  3.55860620e-01, 5.90680857e+00, 3.33589457e+00, 1.26348286e+01,
                  7.99484035e-01, 7.78645752e+00, 3.94760131e+00, 2.68475403e+01,
                  3.66793653e+00, 7.48623952e+00, 6.41873506e+00, 1.24598627e+01,
                  6.03808891e+01, 1.40420660e+01, 3.20433577e-01, 4.90769871e+00,
                  2.64859643e+01, 1.92060974e+00, 9.82495650e+00, 8.52951810e+02,
                  1.77397981e+01, 1.85988499e+01, 1.19103878e+01, 1.04652085e+01,
                  6.05058789e+00, 2.46465783e+00, 1.90930692e+00, 1.46807663e+01,
                  1.33996659e+01, 7.11886064e+00, 4.25787509e+00, 7.22376564e+00,
                  9.52530346e+00, 1.32197738e+00, 1.08783723e+01, 2.43042260e+01,
                  2.61254733e+00, 6.17059868e+00, 1.03999273e+00, 3.55025707e+00,
                  2.59964220e+00, 3.86451242e+00, 3.27217637e+00, 3.49348353e+00,
                  2.00850892e+01, 4.39596044e+00, 9.80431674e+00, 1.60650863e+01,
                  1.30706874e+01, 2.59878321e+00, 5.44593592e+00, 3.96679777e+00,
                  5.55893105e+00, 3.62704517e+00, 4.29500494e+00, 1.88278071e+00,
                  2.44090864e+00, 9.86575053e-01, 7.36859206e+01, 6.38921495e+00,
                  4.38725677e-02, 1.32390595e+01, 8.31431243e+01, 1.71164523e+01,
                  4.23646868e+01, 8.97400746e+00, 1.13659706e+00, 6.52798276e+00,
                  1.49354388e+01, 2.34403173e+00, 1.94479374e+00, 7.28347712e+00,
                  5.78523878e+00, 2.94118681e+00, 2.51627568e+00, 1.52609569e+01,
                  3.42091484e+00, 5.11937967e+00, 5.81578794e+00, 3.13527913e+00,
                  1.27926313e+00, 8.15501952e+00, 1.16534847e+01, 5.73677315e+00,
                  9.28349836e+00, 8.52594333e+00, 4.24350554e+00, 3.50925716e+00,
                  7.24568306e+00, 4.31833896e+00, 1.79979255e+01, 2.58516223e+01,
                  2.91755047e+00, 6.34600402e+01, 2.95245388e+00, 6.61378693e-01,
                  8.04306771e-01, 5.09004862e+00, 1.07071279e+00, 2.00110367e+00,
                  1.14831165e+01, 6.38280647e+00, 3.36021664e+00, 5.63914191e-02,
                  3.27358321e+00, 6.35595200e+00, 3.41602660e-02, 3.39257327e+00,
                  5.90518674e+00, 1.06788316e+01, 2.16043196e+01, 5.69300946e+00,
                  2.54242936e+01, 1.31337069e+01, 4.74805052e-01, 3.17893012e+00,
                  5.68386817e+01, 1.06229279e+00, 1.71115880e+01, 2.40331543e+00,
                  5.62638518e+01, 1.34947583e-01, 4.97729044e+02, 2.17892486e+00,
                  6.06332101e-01, 1.39254107e+01, 3.30030122e+00, 1.22927328e+01,
                  2.38630316e-01, 1.14919233e+01, 7.92218432e+00, 4.96289825e+00,
                  1.19392565e+02, 3.87631891e+00, 2.01986067e+01, 1.66296974e+01,
                  7.73349370e+01, 4.01943124e+00, 2.84116683e+01, 1.09187421e+01,
                  2.70243104e+01, 2.51024948e+01, 9.66511340e-01, 9.92471669e-01,
                  3.93042704e+00, 1.83974120e+01, 8.63172526e-02, 3.56052398e+01,
                  1.95386430e+01, 4.28143808e+01, 2.80084149e+02, 8.10491012e-01,
                  1.59955592e+00, 4.69946958e+00, 2.09853000e+01, 1.29065869e+00,
                  1.03385958e+01, 5.58042565e+00, 1.36891134e+01, 2.07339662e+00,
                  2.34633470e+02, 3.07651440e-01, 8.15758555e+00, 7.59201379e+00,
                  2.80787293e+00, 4.10203586e+01, 1.85376170e+01, 4.18047975e-01,
                  6.35489380e+00, 7.87659490e+00, 4.54827503e+00, 6.21220244e+00,
                  3.73226642e-01, 6.55450216e+00, 6.46165601e+00, 8.98199070e+00,
                  2.47467082e+00, 1.13676416e+00, 1.41909565e+01, 7.11136568e-01,
                  1.75481564e+00, 3.23215785e+00, 2.93313312e+00, 3.15532418e+01,
                  7.98561131e+00, 1.05064553e-01, 4.82809693e+00, 1.76555443e+02,
                  5.32174371e+00, 4.55992185e+00, 3.67397160e+01, 3.36663638e+00,
                  1.32244240e+02, 3.85048211e+00, 8.00407098e+00, 6.96690236e+00,
                  2.30360757e+00, 1.70428638e+00, 2.59184867e+00, 1.50282676e+01,
                  1.28655891e+00, 1.99280409e+00, 8.21201260e+00, 4.33655373e+00,
                  1.46263714e+00, 3.93249313e+01, 7.58318251e-01, 4.17660322e+00,
                  1.97197890e-01, 4.15862987e+00, 3.44106890e-01, 2.22394499e+00,
                  1.67094954e+00, 5.30404024e+00, 4.45536215e+01, 4.04097771e+00,
                  4.41405367e+00, 8.56619848e-01, 6.77150997e+00, 3.51147472e+00,
                  1.79757632e+00, 5.38281513e+00, 8.04053720e+00, 1.31617672e+00,
                  7.29586706e+00, 5.64479222e+00, 1.10124728e+01, 3.51148550e+00,
                  8.48893842e+00, 2.03011523e+00, 1.47222214e+00, 3.08129283e+00,
                  3.28954468e+01, 2.48340395e+02, 9.77060941e+00, 8.99523436e+00,
                  2.92244076e+00, 3.65982422e+00, 3.85351765e+01, 9.08105536e+00,
                  3.61923284e-01, 3.64318543e-01, 8.70516003e-01, 4.89143145e+00,
                  6.43215603e+01, 4.38444148e+00, 8.88800587e+00, 8.78349600e+00,
                  1.42103159e+00, 9.16332164e-01, 4.27483744e+01, 8.38062714e+00,
                  5.03178779e+00, 9.16495297e-01, 2.37194396e-02, 2.55563934e-01,
                  4.50959860e-03, 6.40454158e+00, 1.38176299e+00, 6.97739824e+00,
                  3.54642159e+01, 4.72821367e+00, 2.65709280e+00, 8.76077741e-01,
                  4.83803718e+00, 3.61143493e+00, 2.73947401e+00, 7.55791129e+00,
                  3.36113760e+00, 1.87747487e+00, 2.11189235e+01, 1.42386725e+00,
                  1.49480946e+00, 4.41617610e+00, 1.40467059e+01, 1.54028196e+00,
                  1.11386987e+00, 5.48447166e+00, 9.80053089e+00, 7.68563169e+00,
                  1.85472819e+00, 2.38471552e+00, 4.64038081e-01, 7.02165340e+00,
                  9.78701852e-01, 1.00843213e-01, 1.07605549e+01, 5.15364914e+00,
                  3.31342339e+00, 9.83409701e+01, 1.45463863e+01, 9.22199170e+01,
                  1.38244218e+00, 7.21307641e+00, 1.66068190e+00, 2.82317146e-01,
                  7.86101169e+00, 2.33509479e+00, 4.12230672e+01, 4.72694765e+01,
                  3.57579298e+00, 1.89324697e-01, 1.81055529e+01, 1.79261079e+00,
                  1.12969976e+01, 1.70972330e+01, 8.97754492e-01, 1.31370031e+02,
                  1.16254263e+03, 1.41413955e+02, 1.94467808e+00, 2.41937145e+00,
                  9.68830770e+00, 4.94392776e-01, 1.85254454e+00, 3.28367802e+00,
                  1.96677760e+01, 1.25207408e+01, 3.52465895e+00, 4.03946115e+01,
                  3.39795947e+01, 3.40396859e+01, 7.81154245e+01, 9.05891458e-01,
                  6.47896261e+00, 2.51053336e-01, 2.22186775e+01, 5.77800241e+00,
                  1.59632932e+02, 6.57462608e+01, 2.35329041e+01, 3.52263195e+00,
                  7.93644844e+00, 3.04897607e+00, 1.68828643e+01, 3.00354774e+00,
                  1.49631606e+00, 3.68801452e-01, 5.81127847e+00, 1.52072448e+01,
                  1.32358722e+01, 2.87060781e+00, 1.30582847e+00, 9.14850928e-01,
                  6.19236323e+00, 3.49339832e+00, 1.67438563e+00, 5.56856956e+00,
                  9.23198526e-01, 2.83168019e+00, 6.87703770e+00, 7.02919842e-01,
                  1.61080403e+01, 3.54203298e+00, 4.03103308e+00, 5.45083242e+00,
                  1.47933347e+01, 3.89416062e+00, 3.60912292e+00, 2.66069043e+00,
                  7.51414121e+00, 1.60205492e+01, 3.40643254e+00, 1.65523055e+01,
                  1.09793640e+01, 1.62986461e+01, 2.52740118e+01, 1.03911068e+01,
                  3.36477616e+00, 1.42340968e+01, 2.35035662e+00, 1.71178905e+01,
                  3.77343764e+00, 2.03714255e+00, 3.31015576e+01, 6.33433007e-01,
                  6.14744658e+00, 7.16088069e+00, 2.23041424e+01, 1.02499349e+00,
                  1.97728679e+00, 3.44821524e+01, 2.61349166e+01, 5.25053778e+00,
                  4.14815656e+00, 3.27333328e+00, 2.45511084e+01, 1.71874526e+01,
                  8.09460414e+00, 1.01537964e+00, 5.93238476e+00, 5.35806269e+00,
                  1.70074971e+00, 9.05856906e+00, 8.68542308e+00, 2.12308484e+00,
                  5.90482450e+00, 9.03874533e+00, 2.43132755e+01, 2.00834863e+01]])
        • mu
          (chain, draw)
          float64
          -0.1979 3.452 ... -15.29 -7.206
          array([[-1.97924571e-01,  3.45176103e+00,  3.66898018e+00,
                  -1.02743940e+01,  4.25360730e+00, -2.02111574e+00,
                   4.99512893e+00, -4.89951797e+00,  2.93259999e+00,
                   3.14718356e+00,  1.27127831e-02, -5.89109961e+00,
                  -3.95595294e+00,  7.20764616e+00, -1.13762985e+01,
                  -2.64993320e+00,  4.63740279e+00, -2.61164777e+00,
                  -4.92404586e+00, -5.32221786e-01, -7.24192440e+00,
                  -2.84180113e+00, -5.93344391e-01, -9.75138109e+00,
                   1.48560255e-01, -4.42832119e-01, -1.52289735e+00,
                   6.52718424e+00, -4.55815233e+00,  8.03345649e+00,
                  -1.25949421e+00,  4.09944512e+00, -2.85912239e+00,
                  -3.12320344e-01, -1.25621514e+00,  2.68736028e+00,
                  -2.19802764e+00,  4.40315543e+00,  9.20349072e+00,
                  -3.84608588e+00, -2.21098734e+00,  7.98896705e+00,
                  -2.56405874e+00, -7.55191977e+00, -3.66256916e+00,
                  -1.93900442e+00,  1.22065841e+00,  1.71740829e+00,
                   8.21454272e+00,  1.92083009e+00, -4.55360166e+00,
                   2.24412248e+00, -2.13959890e+00,  9.43831952e+00,
                   9.61207333e+00, -3.95567894e+00, -4.81381220e+00,
                  -4.39614559e+00, -1.56718278e+00, -5.36653851e+00,
                   1.92902328e+00, -5.46437773e+00, -8.28278477e-01,
                  -2.15915746e+00, -5.48922909e+00,  1.13661423e+00,
                   2.09137433e+00, -2.54786877e+00, -2.65724057e+00,
                   2.05729726e+00, -1.61402241e-01, -2.83105628e+00,
                   5.37481879e+00, -7.79670411e+00,  1.23781801e+00,
                  -1.05330598e+01, -4.50752694e+00, -8.14796386e+00,
                  -4.70073053e+00,  3.80565742e+00,  5.50567267e+00,
                   4.16868852e-01, -2.35527277e+00, -8.36613464e+00,
                  -7.13115096e-01,  1.43720177e+00, -6.10898476e+00,
                  -8.81174187e-01, -7.00294828e+00, -6.25292261e+00,
                  -3.70662453e-01,  5.97140466e-01,  1.69662795e+00,
                   6.36365353e+00,  1.95191457e+00, -4.14199908e-01,
                  -9.02638518e+00,  5.15984968e+00, -4.09147662e+00,
                  -5.23406237e+00, -6.09587492e+00, -4.65743036e+00,
                   4.33676745e+00, -9.91340056e+00,  2.83535062e+00,
                   4.70713637e+00, -6.33033245e+00, -2.19378021e+00,
                   5.86431705e+00,  3.46673670e+00, -2.43746040e+00,
                   1.68730344e+00,  3.60685353e+00,  2.88654746e+00,
                  -3.15878724e-01,  1.62471781e+00,  3.35119982e+00,
                   4.63666452e-01,  7.87306500e-01, -9.24725008e-01,
                  -3.38194013e+00,  4.52134311e+00, -2.26543848e-01,
                  -3.44352266e+00,  1.72719800e+00,  2.39885986e+00,
                  -6.50678946e+00, -7.56880421e+00, -5.30732847e+00,
                  -5.17096376e+00, -1.94421141e+00, -6.93298928e-01,
                  -1.52396072e+00, -5.60458995e-02,  4.94155671e+00,
                  -1.07948739e+00, -1.69029823e+00,  1.84554371e+00,
                   6.38458750e-01, -8.40430815e+00, -3.73774329e+00,
                   3.07278534e+00,  2.05623948e-01, -5.27314592e-01,
                   6.15851493e-01, -6.35782747e+00,  1.05558401e+00,
                  -4.61172554e-01,  2.74970370e+00, -1.11008096e+00,
                  -1.06719737e+00, -1.25335382e+00, -1.05161094e+01,
                  -2.79222678e+00, -2.61743694e+00,  1.06859928e+01,
                   4.17430844e+00, -8.61940068e+00,  6.62649786e+00,
                  -3.77297366e+00, -4.79928278e+00,  2.11312406e+00,
                   3.82841892e+00,  1.65150718e+01,  1.28827753e+00,
                   7.69045233e+00,  4.32595573e+00,  5.67468866e+00,
                  -4.26950865e+00,  1.42134184e+01, -3.02203250e+00,
                   7.88690400e+00,  4.70002602e+00,  1.22227407e+01,
                  -9.17601028e+00, -4.89870159e+00,  3.69229719e+00,
                  -7.05443646e+00,  3.16827030e+00,  5.92829164e+00,
                   6.32853189e-01, -4.97531523e+00,  5.35110233e+00,
                   4.84398026e+00, -1.30950889e+00,  3.10966847e+00,
                   5.19944573e+00, -4.09236633e+00, -1.51532902e+00,
                   2.07513611e+00,  1.17597066e+00, -1.32898956e+00,
                  -6.41614907e+00, -7.89735147e+00,  1.50822033e+00,
                   4.09212007e+00,  2.47951153e+00, -1.63800121e+00,
                  -1.86176988e+00, -2.52168837e+00, -6.64242059e+00,
                  -1.02397782e+01, -4.54425137e+00,  2.62436848e+00,
                   1.22193671e+00, -9.38962033e+00, -1.10203324e+00,
                  -7.05103435e+00, -4.46289833e+00,  5.25312798e+00,
                  -3.56515665e+00,  1.26120037e+00,  4.75885172e+00,
                  -2.50167965e+00,  3.80542944e+00,  3.01167210e+00,
                   2.70345411e+00,  5.73690638e+00, -4.54935671e+00,
                  -6.43236445e+00,  7.41097905e+00,  1.35900623e+00,
                   5.04012320e-01, -3.15086965e-01,  1.64858689e+00,
                  -2.06980294e+00, -8.59024295e+00, -4.97349172e-01,
                  -1.80382620e+00,  1.17371261e+01,  2.15827083e+00,
                   2.22745215e+00, -1.20855349e+00, -2.44807351e+00,
                  -9.87085690e+00, -1.34467216e+00, -5.81848641e+00,
                   3.96936369e+00,  6.03001020e+00,  2.48189062e+00,
                  -3.39454396e+00,  8.02506367e+00, -1.08853432e+01,
                  -5.95905160e+00,  5.62999973e+00, -1.33903618e+00,
                   2.43456328e-01,  7.46115585e+00,  7.25904503e+00,
                   5.91408176e+00, -8.78687142e+00, -6.51018263e+00,
                  -4.41948337e+00, -2.48947673e+00, -1.64088207e+00,
                   6.20255356e+00, -9.17992329e+00,  3.82492982e+00,
                   2.63842026e+00, -4.17331044e+00,  1.75196415e+00,
                  -5.04693689e+00,  1.35289027e+00,  7.57024645e+00,
                   7.42244523e-01, -8.30060584e+00, -4.41346052e+00,
                   2.16165760e+00, -5.26439002e+00, -6.91396918e+00,
                   5.37676522e-01,  4.51113679e+00, -8.02857560e-01,
                  -2.33763106e+00, -3.14059882e+00, -3.39669533e+00,
                   9.30930118e-01, -5.37274114e+00,  1.77406778e+00,
                   4.51427847e+00, -4.11358649e+00,  3.99759043e+00,
                   1.53790689e+00,  3.08286549e+00,  1.96950901e+00,
                  -2.33147685e+00,  8.35301298e+00,  3.64283230e+00,
                   3.93723672e+00, -1.55395905e+00, -4.08348595e+00,
                  -1.12488433e+00, -4.94433054e+00,  1.09220685e+00,
                  -2.96159007e+00, -3.82612120e+00,  5.71952703e+00,
                   2.96089980e+00,  6.57383263e+00,  3.43877847e+00,
                   3.23617754e+00, -3.26402642e-01, -1.83070903e+00,
                   2.65271223e+00,  4.20683702e+00,  6.46751652e+00,
                   3.60872783e-01, -8.27036082e+00, -9.63407531e+00,
                   3.26333096e-01,  2.43822818e+00, -7.43272899e+00,
                  -2.69406922e+00,  3.71935806e+00, -5.18549573e+00,
                  -4.51118195e+00, -2.09199225e+00,  5.78108487e+00,
                  -5.89811771e+00,  3.49169444e+00, -5.05185406e+00,
                  -1.20226878e+00,  6.53307013e+00,  4.81768620e+00,
                   4.17257863e+00, -3.86026668e+00,  5.58392228e+00,
                  -4.41510369e+00,  5.57459816e-01,  2.72842246e+00,
                  -7.78855364e+00,  5.68483356e+00,  3.29852882e+00,
                   9.55117660e+00, -6.27973606e+00,  1.78814651e+00,
                   1.39547434e+00,  7.55131835e-01,  3.65522852e-01,
                   4.38405961e+00, -1.68567975e+00, -8.80176186e+00,
                  -5.19047572e+00,  4.07829465e+00,  4.29162615e+00,
                  -1.20809055e+00, -2.34765354e+00, -6.46386071e+00,
                  -6.03662219e-01, -4.66821357e+00, -1.43937731e-01,
                   1.09606189e+00,  6.30828939e+00, -1.30803069e+00,
                  -3.03474141e+00,  3.35965967e-01, -6.33265044e+00,
                   3.28254564e+00,  1.37978799e+00, -2.48652438e+00,
                  -1.84211152e+00, -8.65571630e+00, -2.90481357e+00,
                  -5.34261854e+00,  1.34312306e+00, -2.08973719e+00,
                   6.18252186e+00,  4.09215122e+00, -1.48227522e+00,
                  -9.72847583e+00, -1.06198133e+00,  8.99839205e-01,
                  -9.42087378e-01, -1.78560508e+00, -4.11869577e+00,
                  -1.94607602e+00, -6.34726065e+00,  5.24379982e+00,
                  -2.23697781e+00,  3.40115386e-01,  3.73908939e+00,
                   4.53282894e+00, -2.28989784e+00, -6.71804450e+00,
                  -4.63620303e-01,  1.13621798e+01, -6.37943935e+00,
                  -2.25709706e+00,  1.65004215e+00,  4.45505702e-01,
                  -4.29752873e+00,  3.41480439e+00, -4.48702607e+00,
                   5.83413204e+00,  9.06419203e+00, -2.52112835e+00,
                   5.00974231e+00, -7.78393797e-01,  3.36146623e+00,
                   4.83698962e+00, -1.05169071e+00,  3.66616293e+00,
                  -1.67252497e+00, -3.62323547e+00,  7.80121165e+00,
                  -3.08831078e+00, -5.43366444e+00, -3.69190337e+00,
                   3.04940823e+00,  4.94988152e-01, -1.56235549e+00,
                  -1.31380093e+01, -2.68698571e-01, -7.08968310e+00,
                   7.25984399e+00, -7.94048679e+00, -9.01143028e+00,
                   2.15010800e+00, -1.39225759e+01, -1.92367776e+00,
                  -1.05580966e+01, -5.65026775e-01,  5.79205213e+00,
                  -1.55147165e+00, -6.97345557e+00,  3.81667571e+00,
                  -1.17125097e+00, -8.23705763e+00,  2.03794735e+00,
                  -1.28032492e+00, -1.10053320e+01,  6.43417469e+00,
                  -3.93257893e+00,  5.37706754e-01,  2.38022617e+00,
                   6.33201935e-01,  6.87942708e+00, -4.85099290e+00,
                   3.03039778e+00,  4.28465279e+00, -3.74243269e+00,
                   5.41243454e+00,  4.19264965e+00,  3.94209299e+00,
                   4.19019105e-01,  9.03729243e-01, -8.47680165e-01,
                   5.44887897e+00, -6.64587581e+00,  2.24505549e+00,
                  -1.62886915e+00,  6.52696615e+00,  4.65538080e+00,
                   2.16153384e+00,  8.01812241e+00,  8.87701558e+00,
                  -8.82977615e-01,  7.44374430e+00, -7.26633089e-01,
                   5.07979280e+00, -7.77941048e+00,  5.93222518e+00,
                  -1.22668195e+01,  1.15109144e+00, -1.05951734e+01,
                   1.09823498e+00,  8.38289171e+00, -5.66352195e+00,
                   9.02288722e+00,  6.64762146e+00, -3.59210701e+00,
                   5.01362305e+00, -2.18552082e+00,  8.10170049e+00,
                   3.35098197e+00, -3.67603554e+00,  9.50009626e-01,
                  -2.69213521e+00,  5.97375478e+00,  9.19377263e+00,
                   4.00684514e+00, -5.14242881e+00, -5.04404481e+00,
                   6.80877591e+00,  2.08913991e+00, -3.28593673e+00,
                   6.94325245e+00, -2.76457961e+00, -1.44369907e-01,
                  -3.11771191e+00,  2.59296320e+00, -1.89779512e+00,
                  -3.00382367e+00, -1.49473069e+00, -6.88520684e+00,
                   5.65785904e+00, -4.92529741e-01,  4.68942995e+00,
                  -1.52910780e+01, -7.20569740e+00]])
        • theta
          (chain, draw, school)
          float64
          -9.888 -1.89 2.237 ... 13.34 -21.99
          array([[[ -9.88782452,  -1.89045271,   2.23745711, ...,   3.05783633,
                     4.50876933, -12.02277258],
                  [ 12.52324972,  -0.10257462,  17.90235743, ...,  -6.03914366,
                     5.39459901,   7.07427163],
                  [  3.22949408,   4.20144679,   3.28459753, ...,   3.70696941,
                     3.39716626,   4.14062422],
                  ...,
                  [  2.88020715,   6.85078948,  10.60362223, ...,  -5.47622351,
                     2.56413578,  -9.94645561],
                  [ 10.70735593, -35.010802  , -49.8329035 , ..., -20.31738401,
                   -42.62663544,  -8.45896299],
                  [-55.3145697 , -16.82455975,  -1.67088179, ...,  18.1635401 ,
                    13.33866153, -21.98739496]]])
        • theta_tilde
          (chain, draw, school)
          float64
          -1.76 -0.3073 ... 1.023 -0.736
          array([[[-1.75960441, -0.30734889,  0.44224485, ...,  0.59121882,
                    0.85469606, -2.14729303],
                  [ 1.10830795, -0.43425049,  1.76549973, ..., -1.15955004,
                    0.23736598,  0.44257976],
                  [-1.0836513 ,  1.31291559, -0.94778141, ...,  0.09367097,
                   -0.67021802,  1.16294391],
                  ...,
                  [-0.20016305,  0.23912163,  0.65431562, ..., -1.12467528,
                   -0.23513155, -1.61923862],
                  [ 1.06931022, -0.81106818, -1.42069815, ..., -0.20673093,
                   -1.12430583,  0.28100348],
                  [-2.39544427, -0.47894385,  0.27559038, ...,  1.26318892,
                    1.02294784, -0.73601253]]])
      • created_at :
        2020-06-10T18:19:23.480401
        arviz_version :
        0.8.3
        inference_library :
        pymc3
        inference_library_version :
        3.8

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 1
        • draw: 500
        • obs_dim_0: 8
        • chain
          (chain)
          int64
          0
          array([0])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 495 496 497 498 499
          array([  0,   1,   2, ..., 497, 498, 499])
        • obs_dim_0
          (obs_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • obs
          (chain, draw, obs_dim_0)
          float64
          -25.31 -0.8959 ... 3.422 -20.64
          array([[[-25.31078195,  -0.89588955,  22.6413552 , ...,  24.13451408,
                    16.67999654, -30.23034528],
                  [  4.86375172,  11.18885402,  22.53588377, ..., -13.80804677,
                    -5.73731196,  -4.12169577],
                  [ -1.79113884,   2.53093031,  15.8191744 , ...,   7.61230557,
                    -4.66752285,  23.29882677],
                  ...,
                  [ 28.47079674,  -2.79239653,  14.3904422 , ..., -12.63998944,
                    20.70652864,  -3.05241501],
                  [ 46.65347282, -46.95008753, -41.11688486, ..., -19.96545045,
                   -34.31368027,  -7.26684645],
                  [-45.06736361,  -5.81423829,   1.34788684, ...,  19.91178202,
                     3.42152391, -20.64388589]]])
      • created_at :
        2020-06-10T18:19:23.484023
        arviz_version :
        0.8.3
        inference_library :
        pymc3
        inference_library_version :
        3.8

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • obs_dim_0: 8
        • obs_dim_0
          (obs_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • obs
          (obs_dim_0)
          float64
          28.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
          array([28.,  8., -3.,  7., -1.,  1., 18., 12.])
      • created_at :
        2020-06-10T18:19:23.485040
        arviz_version :
        0.8.3
        inference_library :
        pymc3
        inference_library_version :
        3.8

From PyStan

[8]:
import pystan

schools_code = """
data {
    int<lower=0> J;
    real y[J];
    real<lower=0> sigma[J];
}

parameters {
    real mu;
    real<lower=0> tau;
    real theta_tilde[J];
}

transformed parameters {
    real theta[J];
    for (j in 1:J)
        theta[j] = mu + tau * theta_tilde[j];
}

model {
    mu ~ normal(0, 5);
    tau ~ cauchy(0, 5);
    theta_tilde ~ normal(0, 1);
    y ~ normal(theta, sigma);
}

generated quantities {
    vector[J] log_lik;
    vector[J] y_hat;
    for (j in 1:J) {
        log_lik[j] = normal_lpdf(y[j] | theta[j], sigma[j]);
        y_hat[j] = normal_rng(theta[j], sigma[j]);
    }
}
"""

eight_school_data = {
    "J": 8,
    "y": np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
    "sigma": np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}

stan_model = pystan.StanModel(model_code=schools_code)
fit = stan_model.sampling(data=eight_school_data, control={"adapt_delta": 0.9})

stan_data = az.from_pystan(
    posterior=fit,
    posterior_predictive="y_hat",
    observed_data=["y"],
    log_likelihood={"y": "log_lik"},
    coords={"school": np.arange(eight_school_data["J"])},
    dims={
        "theta": ["school"],
        "y": ["school"],
        "log_lik": ["school"],
        "y_hat": ["school"],
        "theta_tilde": ["school"],
    },
)

stan_data
INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_9d743830ec4a29fb58eb4660d4b9417f NOW.
[8]:
arviz.InferenceData
    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 4
        • draw: 1000
        • school: 8
        • chain
          (chain)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • mu
          (chain, draw)
          float64
          8.801 4.356 5.887 ... 5.811 6.163
          array([[ 8.80085977,  4.35621311,  5.88747459, ...,  7.56510323,
                   3.75692215,  4.24241574],
                 [ 3.88430209,  1.25503637,  8.12161043, ...,  0.77999781,
                   8.88447765,  2.55867698],
                 [ 3.69774758,  5.56187344,  7.18886091, ...,  2.35104484,
                   7.36896537,  7.30112058],
                 [ 4.56370867, -1.9814485 ,  8.93919361, ..., -0.45859494,
                   5.81131473,  6.16295074]])
        • tau
          (chain, draw)
          float64
          1.079 2.76 3.322 ... 3.54 0.5714
          array([[1.07873807, 2.75983947, 3.32167212, ..., 4.65835454, 5.67923053,
                  1.15391559],
                 [0.68602682, 1.9898873 , 1.71348775, ..., 6.32124664, 6.49443423,
                  7.88054963],
                 [6.09793056, 2.08870225, 3.01847687, ..., 0.19977493, 2.0959731 ,
                  2.08265721],
                 [4.80268382, 8.63940768, 7.49279334, ..., 4.94150802, 3.54035862,
                  0.57140337]])
        • theta_tilde
          (chain, draw, school)
          float64
          0.7707 3.4 ... 0.9492 -0.1983
          array([[[ 0.77065058,  3.3999605 ,  0.896277  , ...,  0.85548385,
                    0.56312311, -0.02336804],
                  [-0.23856364,  1.88839417,  0.11615247, ...,  0.20239506,
                   -0.65088377, -0.59082016],
                  [-0.44993014,  0.3660292 , -0.85342255, ..., -0.05060912,
                    1.89747793, -0.29915642],
                  ...,
                  [-1.53738528,  0.34600749,  0.66613118, ..., -0.31358001,
                   -0.13278535, -0.13050197],
                  [ 0.10392075,  1.2781256 ,  0.17946725, ...,  0.73474013,
                    1.59901667, -0.22310606],
                  [ 0.40039   , -0.36919646, -0.41812356, ..., -0.82578604,
                   -0.95433683, -0.70055211]],
          
                 [[ 0.28550956, -1.75918566,  1.08585615, ..., -0.17260057,
                   -0.31717858, -0.15889076],
                  [ 1.12616284,  2.12250411, -1.22377048, ..., -0.50452776,
                    1.09665063,  0.62770833],
                  [-0.82113198,  0.60950151,  0.12629451, ...,  1.18250354,
                    1.03982808,  0.4350411 ],
                  ...,
                  [-0.14425363,  0.18750333,  2.30758557, ...,  0.19605514,
                    0.04511098,  1.31371653],
                  [ 0.70622565,  0.07230275, -1.80811131, ..., -0.30374127,
                    0.73420799, -0.89225914],
                  [ 1.13667967, -0.62298503,  0.70894404, ...,  0.93673866,
                    0.83697246,  1.22364797]],
          
                 [[ 1.71586288,  0.2645208 ,  1.38154111, ...,  1.34611706,
                    0.67924247,  0.6426671 ],
                  [-0.63375751, -0.25986361, -1.85613258, ..., -1.1958948 ,
                    0.65731631, -0.33917202],
                  [-0.25273764, -0.31382369, -0.34433588, ...,  1.56951567,
                   -0.42550589,  0.13231013],
                  ...,
                  [-1.3109662 ,  1.0167199 ,  0.29096078, ...,  1.2091756 ,
                   -0.35967787,  0.28249554],
                  [ 2.40744126, -0.73846363, -0.98632421, ..., -0.79229741,
                    2.01420262,  1.00171644],
                  [ 2.25146098,  0.08915173, -0.37030215, ..., -0.75901238,
                    0.46540678,  0.5400871 ]],
          
                 [[ 0.43838309,  0.06907241,  0.44621424, ..., -0.26691355,
                    1.45697414,  0.66782308],
                  [ 1.38057301,  0.71432475, -0.92534916, ...,  0.23614769,
                    0.48711266,  1.27270678],
                  [ 0.38952426, -0.18324781,  0.28926883, ..., -0.11207212,
                    1.06242534, -1.2021079 ],
                  ...,
                  [-0.57243771,  1.20324745, -2.03671137, ..., -0.31232212,
                    0.68695275,  0.59062609],
                  [ 0.83778081, -0.58047982,  1.78149714, ..., -0.62379571,
                    1.44340525, -0.0475484 ],
                  [ 1.5197586 , -0.90722855,  1.74266398, ..., -1.08440477,
                    0.94915432, -0.19832845]]])
        • theta
          (chain, draw, school)
          float64
          9.632 12.47 9.768 ... 6.705 6.05
          array([[[  9.6321899 ,  12.4685266 ,   9.7677079 , ...,   9.72370277,
                     9.40832211,   8.77565177],
                  [  3.69781575,   9.56787788,   4.67677528, ...,   4.91479099,
                     2.55987838,   2.72564431],
                  [  4.39295419,   7.10330357,   3.05268471, ...,   5.71936768,
                    12.19027412,   4.89377505],
                  ...,
                  [  0.40341755,   9.17692878,  10.66817842, ...,   6.10433636,
                     6.94654197,   6.9571788 ],
                  [  4.34711206,  11.01569209,   4.77615802, ...,   7.92968074,
                    12.83810642,   2.4898514 ],
                  [  4.704432  ,   3.81639419,   3.75993645, ...,   3.28952836,
                     3.1411916 ,   3.43403774]],
          
                 [[  4.08016931,   2.67745355,   4.62922853, ...,   3.76589348,
                     3.66670908,   3.77529877],
                  [  3.4959735 ,   5.47858035,  -1.18012896, ...,   0.251083  ,
                     3.43724753,   2.5041052 ],
                  [  6.71461084,   9.16598381,   8.33801454, ...,  10.14781577,
                     9.90334312,   8.86704803],
                  ...,
                  [ -0.13186495,   1.96525264,  15.36681533, ...,   2.01931073,
                     1.06515544,   9.08432401],
                  [ 13.47101369,   9.3540431 ,  -2.85818235, ...,   6.91184994,
                    13.65274315,   3.08975938],
                  [ 11.51633751,  -2.35078743,   8.14554566, ...,   9.94069244,
                     9.15448   ,  12.20169557]],
          
                 [[ 14.16096028,   5.31077703,  12.12228932, ...,  11.90627594,
                     7.83972096,   7.61668693],
                  [  4.23814271,   5.01909573,   1.68496516, ...,   3.06400529,
                     6.9348115 ,   4.85344408],
                  [  6.42597819,   6.24159135,   6.14949101, ...,  11.92640765,
                     5.90448123,   7.58823597],
                  ...,
                  [  2.08914666,   2.55415999,   2.40917151, ...,   2.59260781,
                     2.27919022,   2.40748037],
                  [ 12.41489748,   5.82116547,   5.30165636, ...,   5.70833131,
                    11.59067987,   9.46853607],
                  [ 11.99014202,   7.48679308,   6.52990814, ...,   5.72035797,
                     8.27040336,   8.42593687]],
          
                 [[  6.66912406,   4.8954416 ,   6.70673459, ...,   3.28180729,
                    11.56109482,   7.77105178],
                  [  9.94588456,   4.18989425,  -9.97591714, ...,   0.05872764,
                     2.22691637,   9.01398426],
                  [ 11.85781836,   7.5661556 ,  11.10662516, ...,   8.0994604 ,
                    16.89972711,  -0.06795243],
                  ...,
                  [ -3.28730045,   5.48726201, -10.52302049, ...,  -2.0019372 ,
                     2.93598756,   2.45998863],
                  [  8.77735924,   3.75620799,  12.11845349, ...,   3.6028542 ,
                    10.92148696,   5.64297636],
                  [  7.03134593,   5.64455729,   7.15871482, ...,   5.5433182 ,
                     6.70530072,   6.0496252 ]]])
      • created_at :
        2020-06-10T18:20:55.257774
        arviz_version :
        0.8.3
        inference_library :
        pystan
        inference_library_version :
        2.19.1.1

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 4
        • draw: 1000
        • school: 8
        • chain
          (chain)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • y_hat
          (chain, draw, school)
          float64
          16.82 11.42 17.62 ... -11.89 1.282
          array([[[ 16.81606234,  11.42314561,  17.62390159, ...,   9.79825611,
                    17.93449592,  20.74301303],
                  [ -2.87371409,   3.26558897,  23.16168449, ...,   5.60727737,
                     9.07428464,  -0.29335618],
                  [ 29.69759628,  27.78756772,  15.23144444, ...,  11.23869389,
                    19.64442795,  16.32327954],
                  ...,
                  [  0.22658945,  14.21873048,  41.77431262, ...,  27.79849965,
                     8.97700113, -10.97758778],
                  [-25.71679369,   7.54290441,  22.1185727 , ...,  -1.9379867 ,
                    24.08319264,  11.10296328],
                  [ 29.8534142 ,  19.97743567,  -2.22962611, ...,  -1.57819509,
                     2.04335776,  -4.69118197]],
          
                 [[ 19.34365445,  -4.00444521, -16.23523472, ...,  13.94222586,
                     8.86119588,  -2.0744115 ],
                  [  4.70865213,  23.04754692,  21.70862296, ...,   0.26881933,
                     8.3109079 , -24.0917072 ],
                  [  8.61267321,   5.41437255, -12.84437828, ...,  30.43257723,
                     1.84297616,   8.86262284],
                  ...,
                  [  3.59843013,   6.09765236,  25.76124843, ..., -10.2115549 ,
                    25.59755363,  22.36298176],
                  [ -5.29619527,  -2.95926353, -29.68418582, ..., -15.42170733,
                    16.63492822,  24.59769265],
                  [ 19.98940386,   3.80606888,  42.7843385 , ...,  34.96627185,
                    14.25740899,  -1.3367825 ]],
          
                 [[  2.14679791,   8.14117178,  21.25441028, ...,  11.52465386,
                     5.80097177, -10.65373129],
                  [ -8.44034177,   7.0589406 , -18.60138882, ...,   8.82950324,
                     8.08712236,  -6.39852626],
                  [ 32.71773469,   8.39087771,  15.51443141, ...,  14.32087597,
                    -1.38048653,   1.96559162],
                  ...,
                  [ -1.62917408,   1.07111862,   8.02957128, ...,   8.58210981,
                   -12.75033047,   9.07205784],
                  [  6.81102221,   1.40270907,  47.46417874, ...,  -1.49189963,
                    23.77214897, -32.30678056],
                  [ -3.58688927,  -9.19334261,   3.48471769, ...,  22.20224365,
                    22.04574534,   9.43498321]],
          
                 [[ 10.88989427,   9.67031316, -19.15138861, ...,   3.89717316,
                     5.08967642,  -3.21365656],
                  [ 16.35385465,  23.58801269, -21.75232011, ...,   1.94421295,
                     0.10598705,  -6.81390168],
                  [ 16.65187106,   5.47807306,  16.66239838, ..., -10.24095255,
                     7.67808457,  23.32038006],
                  ...,
                  [ -5.39983067,   2.9583006 ,   8.89615588, ..., -13.19594644,
                     8.22006103, -10.21126023],
                  [ 11.9101745 ,   6.81738971,  33.3703771 , ...,  -3.27619529,
                    24.69391859, -16.79777889],
                  [  9.5301372 ,  21.03087493,  15.88465758, ...,   1.06856218,
                   -11.8929359 ,   1.28188204]]])
      • created_at :
        2020-06-10T18:20:55.276063
        arviz_version :
        0.8.3
        inference_library :
        pystan
        inference_library_version :
        2.19.1.1

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 4
        • draw: 1000
        • school: 8
        • chain
          (chain)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • y
          (chain, draw, school)
          float64
          -4.377 -3.321 ... -3.859 -3.864
          array([[[-4.37671417, -3.32136228, -4.00991469, ..., -3.63130897,
                   -3.59060827, -3.82535415],
                  [-4.93942464, -3.23381483, -3.80663053, ..., -3.38016268,
                   -4.4135104 , -3.94204744],
                  [-4.86541676, -3.22554395, -3.76307997, ..., -3.40886865,
                   -3.3902882 , -3.88723997],
                  ...,
                  [-5.31936954, -3.22844943, -4.05640831, ..., -3.42449599,
                   -3.8324183 , -3.84855419],
                  [-4.8702312 , -3.26699562, -3.80963006, ..., -3.51526552,
                   -3.35474935, -3.94888271],
                  [-4.83295204, -3.30903641, -3.7807787 , ..., -3.33849472,
                   -4.32544456, -3.92254441]],
          
                 [[-4.89845162, -3.36317113, -3.80520915, ..., -3.34844607,
                   -4.24873977, -3.91370182],
                  [-4.9613161 , -3.25331141, -3.69799587, ..., -3.31915148,
                   -4.28189242, -3.94846464],
                  [-4.63380605, -3.22832122, -3.94260259, ..., -3.6626294 ,
                   -3.54930289, -3.82445749],
                  ...,
                  [-5.38565946, -3.4036145 , -4.35039426, ..., -3.32112717,
                   -4.65546843, -3.82242938],
                  [-4.09608083, -3.23069079, -3.69156654, ..., -3.46125517,
                   -3.31601684, -3.93182941],
                  [-4.23079124, -3.75721763, -3.93415067, ..., -3.64714778,
                   -3.61273975, -3.80937307]],
          
                 [[-4.05258656, -3.25768323, -4.13817498, ..., -3.80834974,
                   -3.73767998, -3.83896065],
                  [-4.88171287, -3.26595258, -3.7343962 , ..., -3.3344376 ,
                   -3.83371561, -3.88812705],
                  [-4.66129633, -3.23698363, -3.85502957, ..., -3.81016597,
                   -3.9530315 , -3.83934681],
                  ...,
                  [-5.11892722, -3.36980949, -3.74867401, ..., -3.3273148 ,
                   -4.45724293, -3.95131096],
                  [-4.16675634, -3.24526023, -3.82613174, ..., -3.4084387 ,
                   -3.42692055, -3.81919966],
                  [-4.19657885, -3.22284053, -3.86890841, ..., -3.40890727,
                   -3.69484888, -3.82902314]],
          
                 [[-4.63811378, -3.26971504, -3.87555205, ..., -3.33834887,
                   -3.42882113, -3.83690906],
                  [-4.35132448, -3.29410816, -3.786573  , ..., -3.32049494,
                   -4.46547446, -3.82307   ],
                  [-4.20603324, -3.22246473, -4.08019302, ..., -3.52510793,
                   -3.22757663, -4.0340564 ],
                  ...,
                  [-5.80231133, -3.25309289, -3.802066  , ..., -3.35407193,
                   -4.35614598, -3.94976063],
                  [-4.44812188, -3.31157248, -4.13794842, ..., -3.34482905,
                   -3.47205036, -3.8716741 ],
                  [-4.6040653 , -3.24926418, -3.89308875, ..., -3.40213025,
                   -3.85937479, -3.86395066]]])
      • created_at :
        2020-06-10T18:20:55.272917
        arviz_version :
        0.8.3
        inference_library :
        pystan
        inference_library_version :
        2.19.1.1

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 4
        • draw: 1000
        • chain
          (chain)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • accept_stat
          (chain, draw)
          float64
          0.9638 1.0 0.9984 ... 0.9816 0.623
          array([[0.9638465 , 1.        , 0.9984371 , ..., 0.98147504, 0.97345614,
                  0.98142691],
                 [0.95030784, 0.99451523, 0.99024004, ..., 0.89369662, 0.9823775 ,
                  0.9890991 ],
                 [0.97217182, 0.99864817, 0.94355364, ..., 0.82019929, 0.97292829,
                  1.        ],
                 [0.95704787, 0.97648727, 0.99909458, ..., 0.998659  , 0.9815929 ,
                  0.6229969 ]])
        • stepsize
          (chain, draw)
          float64
          0.2764 0.2764 ... 0.2731 0.2731
          array([[0.27638304, 0.27638304, 0.27638304, ..., 0.27638304, 0.27638304,
                  0.27638304],
                 [0.30603051, 0.30603051, 0.30603051, ..., 0.30603051, 0.30603051,
                  0.30603051],
                 [0.40097617, 0.40097617, 0.40097617, ..., 0.40097617, 0.40097617,
                  0.40097617],
                 [0.27312733, 0.27312733, 0.27312733, ..., 0.27312733, 0.27312733,
                  0.27312733]])
        • treedepth
          (chain, draw)
          int64
          4 4 4 4 4 4 4 4 ... 3 4 4 4 4 4 4 4
          array([[4, 4, 4, ..., 4, 4, 4],
                 [4, 4, 4, ..., 4, 4, 4],
                 [3, 4, 3, ..., 3, 4, 3],
                 [4, 4, 4, ..., 4, 4, 4]])
        • n_leapfrog
          (chain, draw)
          int64
          15 15 15 15 15 ... 15 15 15 15 15
          array([[15, 15, 15, ..., 15, 15, 15],
                 [15, 15, 15, ..., 15, 15, 15],
                 [ 7, 23,  7, ...,  7, 15,  7],
                 [15, 15, 15, ..., 15, 15, 15]])
        • diverging
          (chain, draw)
          bool
          False False False ... False False
          array([[False, False, False, ..., False, False, False],
                 [False, False, False, ..., False, False, False],
                 [False, False, False, ..., False, False, False],
                 [False, False, False, ..., False, False, False]])
        • energy
          (chain, draw)
          float64
          19.65 17.08 13.29 ... 12.37 14.72
          array([[19.6501434 , 17.07881195, 13.29070373, ...,  8.93538194,
                  12.29961118,  7.19678138],
                 [ 8.84426238,  9.84895256, 14.77525803, ..., 12.35370489,
                   9.67205678,  7.66728697],
                 [11.52204836,  9.48080195, 11.1699379 , ..., 18.41838234,
                  14.78772817, 11.62941587],
                 [ 7.71092746,  9.24555017,  6.98821981, ..., 10.58081723,
                  12.37474199, 14.71998465]])
        • lp
          (chain, draw)
          float64
          -12.88 -8.832 ... -5.587 -9.343
          array([[-12.88137893,  -8.8319153 ,  -6.48855593, ...,  -5.43677471,
                   -4.0330844 ,  -4.6496315 ],
                 [ -5.97351824,  -6.9490221 ,  -6.14793864, ...,  -6.89176892,
                   -4.88146623,  -4.37360644],
                 [ -6.16694264,  -5.66030842,  -4.64701238, ...,  -8.85576565,
                   -9.41927215,  -6.90323691],
                 [ -3.13060803,  -4.68668125,  -3.99299316, ...,  -6.48974414,
                   -5.58723251,  -9.34270347]])
      • created_at :
        2020-06-10T18:20:55.267462
        arviz_version :
        0.8.3
        inference_library :
        pystan
        inference_library_version :
        2.19.1.1

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • school: 8
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • y
          (school)
          float64
          28.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
          array([28.,  8., -3.,  7., -1.,  1., 18., 12.])
      • created_at :
        2020-06-10T18:20:55.238703
        arviz_version :
        0.8.3
        inference_library :
        pystan
        inference_library_version :
        2.19.1.1

From Pyro

[9]:
import pyro
import pyro.distributions as dist
import torch
from pyro.infer import MCMC, NUTS, Predictive

pyro.enable_validation(True)
pyro.set_rng_seed(0)

draws = 500
chains = 2
eight_school_data = {
    "J": 8,
    "y": torch.tensor([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
    "sigma": torch.tensor([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}


def model(J, sigma, y=None):
    mu = pyro.sample("mu", dist.Normal(0, 5))
    tau = pyro.sample("tau", dist.HalfCauchy(5))
    with pyro.plate("J", J):
        theta_tilde = pyro.sample("theta_tilde", dist.Normal(0, 1))
        theta = mu + tau * theta_tilde
        return pyro.sample("obs", dist.Normal(theta, sigma), obs=y)


nuts_kernel = NUTS(model, jit_compile=True, ignore_jit_warnings=True)
mcmc = MCMC(
    nuts_kernel,
    num_samples=draws,
    warmup_steps=draws,
    num_chains=chains,
    disable_progbar=True,
)
mcmc.run(**eight_school_data)
posterior_samples = mcmc.get_samples()
posterior_predictive = Predictive(model, posterior_samples).get_samples(
    eight_school_data["J"], eight_school_data["sigma"]
)
prior = Predictive(model, num_samples=500).get_samples(
    eight_school_data["J"], eight_school_data["sigma"]
)

pyro_data = az.from_pyro(
    mcmc,
    prior=prior,
    posterior_predictive=posterior_predictive,
    coords={"school": np.arange(eight_school_data["J"])},
    dims={"theta": ["school"]},
)
pyro_data
[9]:
arviz.InferenceData
    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 2
        • draw: 500
        • theta_tilde_dim_0: 8
        • chain
          (chain)
          int64
          0 1
          array([0, 1])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 495 496 497 498 499
          array([  0,   1,   2, ..., 497, 498, 499])
        • theta_tilde_dim_0
          (theta_tilde_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • mu
          (chain, draw)
          float32
          6.783849 3.0570068 ... 0.92949176
          array([[ 6.783849  ,  3.0570068 , -0.5898714 ,  7.692052  ,  5.978842  ,
                   7.083586  ,  6.0941653 ,  8.367151  ,  5.2405605 ,  2.639793  ,
                  10.008863  ,  6.0008774 ,  5.048078  ,  1.7424315 ,  2.6212542 ,
                   5.87026   ,  4.5748415 ,  1.0863168 ,  5.662515  ,  1.564056  ,
                   3.2569106 ,  2.1572587 ,  5.9424744 ,  1.2574946 ,  7.5349984 ,
                   3.0202703 ,  2.4996028 ,  3.3100448 ,  3.2369874 ,  5.179661  ,
                   1.4572364 , -0.03877497, -1.1503081 ,  1.7937964 ,  1.7937964 ,
                   6.6380773 ,  1.5952408 ,  7.8001666 ,  6.2870593 ,  3.2218194 ,
                   6.0440335 ,  3.8866324 ,  4.218601  ,  4.218601  ,  7.2325306 ,
                   7.5369225 , 12.167865  ,  7.2303514 ,  7.0910425 ,  2.2544699 ,
                  13.885392  ,  2.3582263 , -0.71636176,  4.0944424 ,  8.234982  ,
                   4.7547674 ,  7.5123987 ,  1.0010346 ,  1.463587  ,  5.0094767 ,
                   6.3490815 ,  4.3477235 ,  2.9339297 ,  5.3828955 ,  1.4211316 ,
                   3.9312172 ,  3.2402444 ,  6.4016495 ,  6.6994824 ,  3.5397    ,
                   4.8213353 ,  5.420148  ,  4.641708  ,  5.0392356 ,  3.5072942 ,
                   4.488197  ,  5.82481   ,  3.192687  ,  7.916957  ,  2.268492  ,
                   5.9801583 ,  6.9189725 , 12.165862  , -2.8586159 ,  9.570917  ,
                   7.068532  ,  2.0816557 ,  6.644463  , -1.9028682 , 10.164826  ,
                   2.5184588 , 11.621914  , -3.3529563 , 10.299711  ,  4.5834465 ,
                   4.585137  ,  7.91378   ,  2.8814616 ,  5.1396675 ,  4.668864  ,
                   3.4275546 ,  4.9457726 ,  3.6325824 ,  5.336408  ,  6.201971  ,
                   6.2212915 ,  0.6339596 ,  7.687422  , 12.570242  , 12.476558  ,
                  10.869892  ,  6.915905  ,  5.5935144 ,  6.058858  ,  1.7806189 ,
                   9.691803  ,  1.2325222 , 10.002609  ,  6.168408  ,  9.982995  ,
                  -0.51718354,  6.5104423 ,  2.9149487 ,  1.4453427 ,  4.3771286 ,
                   4.527439  ,  1.4286865 ,  3.5170612 ,  7.5207043 ,  6.6093435 ,
                   0.9016738 ,  8.855167  ,  4.44285   ,  6.2064247 , 11.12649   ,
                  10.901761  , 10.992046  ,  1.6697562 ,  9.535236  , -1.4199173 ,
                   0.04521966,  0.24071217,  1.0354244 ,  3.8727565 ,  6.546321  ,
                   7.4994783 ,  5.1963906 ,  2.2472491 , -1.4566408 ,  3.2481778 ,
                   1.5054731 ,  5.427044  ,  0.7663537 , 12.421476  , 13.937447  ,
                   9.55212   ,  8.892584  ,  4.5370684 ,  6.597247  ,  3.521164  ,
                   6.200644  , -0.6878598 , -0.5076442 , -1.1443609 , -2.024046  ,
                   7.497966  ,  3.9299464 ,  2.1074817 ,  7.6489606 , -0.5676765 ,
                   8.88996   ,  1.7325966 ,  3.6853108 ,  9.022504  ,  3.554699  ,
                   6.0461593 , 10.99902   , -4.534336  , -1.3497578 ,  3.4103231 ,
                   3.4103231 ,  5.511337  ,  1.5036378 ,  6.0223374 ,  5.0781465 ,
                   7.4995213 ,  2.2854679 ,  5.5526514 ,  4.916196  ,  2.576561  ,
                   5.576095  ,  4.371717  , 13.234244  , 13.360312  , -0.45095968,
                   2.989245  ,  0.6203029 ,  7.7407403 ,  9.276141  ,  4.255246  ,
                   6.0797963 ,  7.8773675 ,  2.5528507 ,  2.1499953 ,  6.2999554 ,
                   2.9320016 ,  5.145282  ,  4.0042167 ,  4.7150197 ,  2.9001827 ,
                   3.637968  ,  3.0349693 ,  3.6715143 ,  1.2648342 ,  2.0227237 ,
                   1.0630711 ,  5.546765  ,  3.8676581 ,  3.0002105 ,  2.6321206 ,
                   4.190834  ,  5.7021546 ,  5.8634467 ,  0.2976514 , -0.47097135,
                  -1.0752056 ,  4.7460985 , -0.6505427 ,  5.6235523 , -0.9203634 ,
                  -1.8839953 , 11.195079  , -2.0718043 , 11.193365  ,  6.1056333 ,
                   8.325111  ,  9.075426  ,  2.9479647 ,  7.128322  ,  4.3343573 ,
                   3.1772745 ,  5.592222  ,  7.5314674 , -3.0730538 ,  3.9833744 ,
                   9.110682  ,  4.5988865 ,  2.8390033 ,  3.4741888 ,  4.0355644 ,
                   3.4970965 ,  0.71459496,  7.2869844 ,  3.6135454 ,  9.620527  ,
                   1.0082316 ,  7.475091  ,  1.0405822 ,  4.5348783 ,  3.8841453 ,
                   4.7387238 ,  4.521943  ,  4.521943  ,  3.539055  ,  6.8544626 ,
                  11.370565  ,  4.756797  ,  4.6440043 ,  6.966434  ,  7.002037  ,
                   9.16461   ,  5.50093   ,  6.000969  ,  1.3224025 ,  6.746578  ,
                   3.1069808 ,  4.3904467 ,  5.1858315 , -0.6927078 ,  7.3248353 ,
                   0.03497177,  2.7320523 ,  4.0992765 ,  1.4401541 ,  3.696537  ,
                   6.4522524 ,  4.343199  , -1.7796711 ,  9.775927  ,  8.519873  ,
                   7.5724382 ,  2.1690316 ,  0.6314293 ,  2.6643667 ,  7.1365185 ,
                   8.02526   ,  0.5847881 ,  6.0416284 ,  1.4256818 ,  8.6619425 ,
                   2.8416598 ,  3.5279734 ,  5.7481217 ,  5.685895  ,  3.817007  ,
                   3.817007  ,  5.1601176 ,  4.495685  ,  2.047713  ,  2.5250795 ,
                   6.463599  ,  7.9371533 , -3.1092994 ,  1.6143876 ,  1.0753083 ,
                   8.186201  ,  5.4840565 ,  3.3782108 ,  6.6359487 ,  0.73560786,
                  -2.5476358 ,  2.1959705 ,  0.595925  , -0.6245699 ,  8.363325  ,
                   7.2956586 ,  1.3452858 ,  7.595389  ,  1.9837761 , -2.1932921 ,
                   5.130442  ,  3.8775177 ,  3.8775177 ,  3.9545794 ,  3.3309066 ,
                   4.0000944 ,  7.8284636 ,  9.910145  ,  0.29044223,  0.4511162 ,
                   4.23416   ,  6.625504  ,  6.7739162 ,  5.979492  ,  2.0962138 ,
                   7.1208596 ,  1.2915809 ,  2.0792012 ,  6.7928405 ,  4.659316  ,
                   3.5058026 ,  2.5944214 ,  7.936224  ,  7.7682953 ,  7.1779675 ,
                   6.921358  ,  0.8594191 , -0.21582747,  0.5738251 ,  2.7562642 ,
                   3.674602  ,  0.5121915 ,  1.0169942 ,  7.307401  ,  6.4692693 ,
                   8.035346  ,  6.3669305 ,  5.8459167 ,  4.03193   ,  7.025049  ,
                   6.2521224 ,  1.1102605 ,  3.404097  , -1.5265621 ,  9.016952  ,
                  11.493106  , -0.57146204, -0.26515374,  7.4198837 ,  6.505427  ,
                   7.2936172 ,  9.671284  ,  2.9167275 ,  2.2982335 ,  7.3781447 ,
                   2.1675684 ,  5.190227  ,  5.3436894 ,  3.0521636 ,  6.544801  ,
                   4.743841  ,  5.7023606 ,  6.8151307 ,  5.6628094 ,  3.9610717 ,
                   5.13286   ,  1.6667626 ,  6.377818  ,  2.9189663 ,  5.914687  ,
                   5.556989  , 12.396165  ,  0.9704962 ,  7.037617  ,  8.90337   ,
                   4.53032   ,  5.2621    ,  6.3007636 ,  1.6994746 , -4.1169577 ,
                   0.44233608,  8.0539665 ,  4.4645185 ,  1.6229515 ,  6.553206  ,
                   7.863461  ,  2.2408123 ,  6.6904135 ,  3.169836  ,  5.7995133 ,
                   5.9354954 ,  4.294053  ,  3.3903077 ,  8.167379  ,  0.7955775 ,
                   4.042009  ,  7.1713643 ,  2.5641007 ,  9.766011  ,  1.7654216 ,
                   6.607266  ,  5.0007186 ,  9.228579  ,  0.11804408,  4.6933355 ,
                   8.756182  ,  7.6457686 , 11.668673  , -2.2822227 ,  5.744774  ,
                  -0.12102944,  5.706559  ,  6.738437  ,  3.9768252 ,  0.6605184 ,
                   1.1702331 ,  7.049793  ,  4.7348275 ,  3.3859143 ,  5.335453  ,
                   5.6728067 ,  8.422111  ,  0.6059617 ,  8.701169  ,  1.3406711 ,
                   0.9726557 ,  2.9391463 ,  8.847219  ,  0.65883195, -1.1129549 ,
                   4.2620173 ,  4.603801  ,  6.1635494 ,  4.814609  ,  4.5336676 ,
                  10.157522  ,  2.3478928 ,  8.260862  ,  4.5819983 ,  5.691238  ,
                   5.3385615 ,  3.9145231 ,  3.366712  ,  4.9146166 ,  4.2341347 ,
                   4.2132525 ,  0.06960184,  5.7912407 ,  7.7237253 ,  8.238167  ,
                  -1.5925429 , -1.8350666 ,  2.7601335 ,  5.2639394 ,  1.3687866 ,
                   1.4656156 ,  4.4150705 ,  0.8827308 ,  1.5304792 ,  7.2156863 ,
                   7.9426675 ,  4.7031536 ,  2.7878287 ,  3.0513043 ,  1.1879033 ,
                   3.9434485 ,  0.61285603, -1.3296754 ,  2.951462  , -0.25293034],
                 [ 5.01953   ,  6.86166   ,  6.6249776 ,  2.2893884 ,  2.501866  ,
                   8.285073  ,  3.7216325 ,  4.7185307 ,  5.471057  ,  2.2488348 ,
                   5.539174  ,  6.0150375 ,  2.0376778 ,  3.660337  ,  1.6074322 ,
                   2.8387644 ,  4.8960958 ,  3.3996067 ,  7.467748  ,  4.651307  ,
                   6.6853914 ,  8.318576  ,  7.023429  ,  6.5320916 ,  7.9992576 ,
                   7.2837024 ,  4.562793  ,  6.547352  , -0.11292058,  7.4648447 ,
                   0.98815346,  4.535407  ,  5.8668675 ,  4.8986874 ,  2.8843725 ,
                   3.232449  ,  2.6490922 , -2.0015569 , -2.0015569 , -0.9957659 ,
                  -0.9957659 ,  0.3136965 ,  3.6559486 ,  3.5627646 ,  1.8010818 ,
                   6.344411  ,  4.7709913 ,  5.2192707 ,  3.2569563 ,  3.880964  ,
                   4.206388  ,  3.2617676 ,  4.079238  ,  2.3552814 ,  3.5103083 ,
                   4.422537  ,  7.6496224 ,  1.7483644 ,  5.4506264 ,  3.694887  ,
                   2.9585373 ,  3.606896  ,  2.6271925 ,  2.4373152 ,  3.0032928 ,
                   2.8940313 ,  7.236042  ,  5.4723234 ,  5.602808  ,  4.8854675 ,
                   3.133181  , -1.9972157 , -5.426025  ,  0.74136853,  2.1391473 ,
                   7.446571  ,  3.438631  ,  4.4135585 ,  2.515184  ,  7.4213567 ,
                   1.4862064 ,  9.58293   ,  2.3712258 ,  9.991231  , 11.811281  ,
                  -3.8299305 , 10.42727   ,  4.5649595 ,  4.0661554 , 12.225602  ,
                   5.1727004 ,  5.384991  ,  2.5262818 ,  2.6618812 ,  4.545309  ,
                   5.200153  ,  4.7776184 ,  0.37785053,  2.9929814 ,  5.422091  ,
                   6.1752453 ,  7.7365675 ,  1.2166401 ,  3.3863912 ,  6.6130266 ,
                   8.373728  ,  7.0688004 ,  5.1593804 ,  8.469555  ,  4.330571  ,
                  -1.7626251 , 12.750014  ,  9.7615    ,  6.4595337 ,  8.6939125 ,
                   2.2231188 ,  5.390884  ,  0.97161454,  4.505579  ,  6.609976  ,
                   4.9074917 ,  4.2184486 ,  6.618556  ,  2.004937  ,  5.4137464 ,
                   9.630217  ,  9.768252  ,  0.30616486,  3.3912468 ,  7.838382  ,
                   9.576023  ,  7.655735  ,  0.18133971, -3.5502794 , 12.7816515 ,
                   6.2193003 ,  6.8971252 ,  2.8146944 ,  6.2655287 ,  2.7793994 ,
                   6.990551  ,  4.122216  ,  7.902957  ,  2.0129812 ,  3.2262692 ,
                   2.7485383 ,  9.244148  ,  7.6056643 ,  5.710777  ,  2.5418003 ,
                   3.4473598 ,  4.393044  ,  3.6912231 ,  6.887758  ,  7.915879  ,
                   8.873672  ,  5.941959  ,  2.1800964 ,  0.72718906,  6.024666  ,
                   2.1498783 ,  1.6291099 ,  9.088835  , -0.6355481 ,  8.986781  ,
                  13.685892  , -4.462116  , 12.183017  , -2.3599992 ,  6.3404007 ,
                   2.0727506 ,  4.6059237 ,  2.2072875 ,  4.4966164 ,  8.327364  ,
                   9.140227  ,  4.9690924 ,  1.7394838 ,  0.86819786,  5.5950966 ,
                   2.6679792 ,  2.9878035 ,  1.293262  ,  5.688295  ,  2.998148  ,
                   7.8103237 ,  2.1600375 ,  0.8984237 ,  3.8629336 ,  7.250372  ,
                   5.4487286 ,  9.825451  ,  9.6626625 ,  3.5370805 ,  2.28778   ,
                   0.7985786 ,  6.5033493 ,  5.7602005 ,  2.1282008 ,  0.7583219 ,
                  -0.2883258 ,  4.04663   ,  4.0531526 ,  7.637555  ,  4.522324  ,
                   1.8140192 ,  6.2982025 ,  0.8498249 ,  4.9770107 , 10.625928  ,
                   2.4482574 ,  1.7317593 ,  2.473702  ,  3.3864214 ,  5.2274213 ,
                   7.1590877 ,  4.082163  ,  4.655895  ,  4.341129  ,  0.72216916,
                   7.632001  ,  5.273179  ,  7.0966406 ,  3.9848332 ,  6.7652764 ,
                  -1.8530495 ,  4.807021  ,  3.7115476 ,  7.7180634 ,  5.495058  ,
                   3.5686898 ,  8.432459  , -3.9393754 ,  3.5627987 ,  1.3835332 ,
                   3.4305634 ,  5.2384458 ,  4.813102  ,  3.7107148 ,  5.8590145 ,
                   7.921546  ,  2.628134  ,  2.35359   ,  4.0655026 ,  3.800044  ,
                   3.1461186 ,  5.714904  ,  5.1543646 ,  3.2590818 ,  3.7851493 ,
                   4.40026   ,  2.7656972 ,  1.0225668 ,  7.9855137 ,  2.9293344 ,
                   4.256064  ,  5.404146  ,  7.5405574 ,  9.850468  , 10.078182  ,
                   6.9839487 ,  8.5010395 , 11.371491  ,  3.3040867 ,  3.5877137 ,
                   1.6272161 ,  1.6272161 ,  5.909365  ,  5.780271  ,  5.5829563 ,
                   4.555645  ,  4.3025413 ,  4.9703617 ,  3.4080243 ,  0.05362892,
                   5.641428  ,  1.9199136 ,  0.4426855 ,  9.342329  ,  2.4715855 ,
                   0.20299262,  7.053833  ,  3.064495  ,  3.7879605 ,  3.0975132 ,
                   4.8171186 ,  4.1754603 ,  1.8580515 ,  3.4130657 ,  1.8592646 ,
                   5.972606  ,  2.600781  ,  5.1370234 ,  3.590805  ,  1.6839093 ,
                   1.1044543 , 11.325514  , 11.263687  ,  3.0054102 ,  4.2464194 ,
                  -1.2235668 ,  0.78690815,  8.217627  ,  8.289513  ,  1.818387  ,
                   7.193574  ,  5.6828175 ,  9.229635  ,  1.8125782 ,  6.0123167 ,
                   3.310267  ,  3.2328024 ,  8.0518055 ,  0.5462723 ,  5.6560984 ,
                   7.22637   ,  8.11613   ,  3.7949753 ,  7.096421  , 10.765428  ,
                   0.62853765,  6.8455167 ,  1.8135126 ,  4.342347  ,  5.897304  ,
                   3.0075347 ,  1.4480636 ,  6.296116  ,  7.323115  ,  2.1111772 ,
                   3.2788057 ,  4.3963056 ,  2.1767483 ,  4.343244  ,  1.7362591 ,
                   8.032246  ,  7.7730284 ,  2.500092  ,  7.870913  , -3.3032596 ,
                   4.2814445 ,  3.4301393 , 10.24017   , -0.06418872,  5.7352066 ,
                   5.756984  ,  5.756984  ,  2.188118  ,  5.0771995 ,  1.7392151 ,
                  10.904758  ,  9.412046  ,  7.786703  ,  8.769625  , 10.503181  ,
                   8.57885   ,  6.9199967 ,  5.4401836 , -0.05953297,  8.981047  ,
                   9.556315  ,  3.1879342 ,  6.2667456 ,  7.8490686 ,  7.600093  ,
                   7.9399824 ,  0.6109712 ,  6.932536  ,  2.7567782 ,  1.5435878 ,
                   4.8659782 ,  2.2375255 ,  8.436639  ,  9.785013  ,  8.592904  ,
                   8.077721  , -0.98542786,  0.47609437,  4.7859526 , -1.187131  ,
                   7.878492  ,  9.416552  ,  1.2292858 ,  5.719812  ,  7.2965436 ,
                   1.962739  , -0.49165836,  5.951705  ,  1.9709172 ,  0.49937028,
                   1.8703003 ,  5.446128  ,  4.893553  ,  4.086196  ,  6.650732  ,
                   2.2123806 ,  2.0845377 ,  7.724782  ,  7.0939484 ,  9.294254  ,
                   0.98116875, 11.221153  , -0.876735  ,  1.3594122 ,  7.842224  ,
                   8.8228245 ,  8.8228245 , 10.224634  ,  7.027872  ,  6.7001348 ,
                   7.376293  ,  9.412687  , -2.8747458 ,  1.0567542 ,  7.480833  ,
                  10.921535  ,  6.2435284 ,  5.193436  ,  6.8472857 ,  3.895755  ,
                   6.2523193 ,  3.9274454 ,  2.3286366 ,  4.988546  ,  4.2868986 ,
                   7.0591617 ,  2.0112956 ,  6.0083036 ,  0.5485797 ,  2.927389  ,
                   8.296615  ,  0.8524151 ,  8.771065  ,  0.8508061 ,  7.5617332 ,
                   4.0908194 ,  6.449942  ,  5.5285096 , -1.5314658 ,  4.6953344 ,
                   4.931533  ,  6.3189793 ,  4.447262  ,  4.547436  ,  6.949565  ,
                   2.027462  ,  4.97022   ,  4.3807526 , 10.430753  ,  3.2305171 ,
                   0.36104214, 10.798279  , -1.6254423 ,  4.7359886 ,  2.0681913 ,
                   3.7673833 ,  1.9625635 ,  4.2347145 ,  7.492998  ,  6.4289722 ,
                   4.327282  , -0.13930517,  2.281067  , -1.5606796 , -0.6715053 ,
                  -2.6402383 ,  6.4653087 ,  1.9133025 ,  5.9235144 ,  8.07356   ,
                   5.0766296 ,  5.6559167 , 10.879023  , -0.92014146,  2.5594158 ,
                   5.5791693 ,  2.8021357 ,  1.2819654 , -2.5959618 , -0.8181571 ,
                   1.8510228 ,  4.257959  ,  9.037647  ,  1.8694059 ,  9.915788  ,
                   5.596039  ,  2.743896  ,  7.2139883 ,  4.4983315 ,  3.314092  ,
                  10.760844  , -1.5691249 ,  7.673089  ,  2.6870704 ,  2.4335454 ,
                  -0.2063955 , -0.75785524, -1.10085   ,  8.008105  ,  0.92949176]],
                dtype=float32)
        • tau
          (chain, draw)
          float32
          2.8592596 7.631564 ... 4.101541
          array([[ 2.8592596 ,  7.631564  ,  2.2398646 ,  2.2167501 ,  3.1840062 ,
                   7.012798  ,  3.243187  ,  6.973709  ,  5.5824986 ,  0.7016568 ,
                   5.86172   , 19.530476  ,  0.25236988,  3.668568  ,  1.5498195 ,
                   0.8107503 ,  1.0509298 ,  7.2098413 ,  1.8983476 ,  5.2955256 ,
                   7.7060432 ,  0.43670726,  3.6594412 ,  6.322126  ,  0.20263568,
                   3.1838627 ,  2.1906252 ,  3.6247058 ,  3.6476884 ,  8.569651  ,
                   0.8154066 ,  0.52646595,  8.347277  ,  5.3391485 ,  5.3391485 ,
                   4.3533516 ,  2.2721968 ,  4.044897  , 12.670698  ,  3.6306577 ,
                   1.7800876 ,  0.8172901 , 10.408458  , 10.408458  ,  8.752845  ,
                   2.7025979 ,  1.8058288 ,  0.77591455,  4.6208324 ,  1.3864799 ,
                   4.8308764 ,  5.2640085 ,  2.2747922 ,  2.1527889 ,  0.6709348 ,
                   0.40966344,  0.76452506,  1.7523602 ,  9.632993  ,  0.71305096,
                   1.2565391 ,  7.3918915 ,  1.9825102 ,  4.3520317 ,  4.191029  ,
                   4.46019   ,  6.5468745 ,  1.7655234 ,  2.4890428 ,  0.13036194,
                   4.1576633 ,  3.6138592 ,  2.5137105 ,  7.9432316 ,  1.4701631 ,
                   4.3312316 ,  3.2743263 ,  6.1689467 ,  0.81546783,  2.3457444 ,
                  14.765036  ,  2.7969723 ,  0.6444865 ,  5.056386  ,  6.6326447 ,
                   3.3019314 ,  3.4695005 , 14.173468  ,  1.0817696 ,  1.9358197 ,
                   6.57442   ,  0.21757841,  1.6629736 ,  2.837197  ,  8.087209  ,
                   0.923576  ,  1.5801088 ,  3.2785625 ,  1.1708685 ,  5.65828   ,
                   2.544188  ,  0.97468114,  0.85679036,  0.4686036 ,  1.2682633 ,
                   1.0238816 ,  1.0111494 ,  3.2353783 ,  5.850848  ,  2.6748486 ,
                   6.8615456 ,  1.0207653 ,  5.1171284 ,  4.7231007 ,  0.9388937 ,
                   1.1121522 ,  0.19136462,  2.5782864 ,  6.664866  ,  1.035229  ,
                   1.2018548 ,  3.5486271 ,  0.26484078,  0.5413486 , 10.383554  ,
                   6.841315  ,  1.663987  ,  1.40886   ,  1.4120247 ,  6.9056168 ,
                   1.4446397 ,  2.328224  ,  2.377081  ,  3.0902762 ,  1.1421281 ,
                   1.1183867 ,  0.9663997 ,  0.72247726,  0.4770038 ,  9.449483  ,
                   3.4366267 ,  1.8293209 ,  5.91921   ,  1.5030367 ,  1.8295302 ,
                   1.9259436 ,  1.0454125 ,  1.1833336 ,  1.635451  ,  3.1804576 ,
                   7.3813477 ,  0.15226473,  9.872404  ,  0.6245333 ,  2.2530851 ,
                   3.5460145 ,  4.784728  ,  3.6828964 ,  1.7373091 ,  1.3222244 ,
                   1.2164129 ,  3.2084877 ,  5.9633555 ,  8.61425   ,  4.7127013 ,
                   1.0490998 ,  2.031085  ,  0.84674907,  1.4061344 ,  0.20833626,
                   1.1506217 ,  8.719571  ,  0.5209326 ,  3.2316248 ,  4.3853264 ,
                   4.2003636 ,  2.0493677 , 10.459623  , 10.027447  ,  5.8418946 ,
                   5.8418946 ,  3.1374278 ,  3.4132574 ,  3.4001408 ,  6.9404526 ,
                   0.6055962 ,  2.6735137 ,  5.0053363 ,  2.393575  ,  4.3127356 ,
                   7.9282527 ,  4.0160623 ,  6.3807807 ,  4.9094033 ,  5.3358846 ,
                   1.5355688 ,  2.814463  ,  0.20154344,  0.16425201,  2.7684138 ,
                   0.79762113,  0.29586637,  8.217145  ,  2.5801165 ,  0.62110734,
                   5.5564575 ,  0.03571094,  9.594197  ,  1.6323905 ,  6.1980906 ,
                   5.9835644 , 10.406311  ,  1.9029803 ,  4.983942  ,  1.1461568 ,
                   8.874212  ,  2.818826  ,  1.3390121 ,  1.8619214 ,  6.0745525 ,
                   5.101248  ,  1.0643479 ,  1.7463428 , 13.184822  ,  6.307802  ,
                   6.2804346 ,  1.8698411 ,  1.3450637 ,  5.679282  ,  3.7104957 ,
                   1.4926912 ,  1.3450874 ,  1.6143674 ,  3.5736926 ,  4.833857  ,
                   0.38555366,  1.7992418 ,  7.924101  ,  0.5311662 ,  1.0728621 ,
                   6.104986  ,  0.41169518,  9.873746  ,  0.6301795 ,  0.6971753 ,
                   0.433702  ,  1.6750252 ,  4.7702184 ,  1.1450185 ,  9.231825  ,
                   0.65097904,  0.07083836,  7.7014275 ,  1.1763483 ,  3.9216068 ,
                   0.7965546 ,  7.643338  ,  0.3307356 ,  1.5628933 ,  8.430889  ,
                   2.0809162 ,  9.241798  ,  9.241798  ,  4.945677  ,  1.0078614 ,
                   1.0361626 , 10.885583  , 12.564192  ,  0.33511108,  4.6200314 ,
                   4.940873  ,  0.5206075 ,  0.07736349,  0.08582618,  1.9981915 ,
                   1.7438189 ,  1.5340894 ,  0.7772387 ,  6.601632  ,  2.115645  ,
                   8.213202  ,  5.2723393 , 11.72069   ,  0.9106035 ,  0.85000837,
                  10.724954  ,  3.2172287 ,  2.224444  ,  4.3728848 ,  6.769486  ,
                  12.659085  ,  6.2303095 ,  1.7800417 ,  0.41352934,  4.2141705 ,
                   2.3804212 ,  1.9563856 ,  2.9715116 ,  1.8923243 ,  3.1873477 ,
                   3.2488613 , 11.12932   ,  1.2553946 ,  0.72405314,  8.201361  ,
                   8.201361  ,  2.594084  ,  4.2437234 ,  1.8843505 ,  1.5556631 ,
                   9.879009  , 13.189886  ,  0.6889656 ,  4.8971453 ,  2.709153  ,
                   5.6291595 ,  3.035018  ,  8.095402  ,  2.2264924 ,  6.9823604 ,
                   8.809837  ,  2.8444104 ,  7.2972403 ,  4.9063    ,  8.416786  ,
                   6.3838606 ,  3.103317  ,  3.3709526 ,  3.7451754 ,  1.5255952 ,
                   6.1873636 , 18.791533  , 18.791533  ,  0.5587105 ,  4.3095994 ,
                   6.199546  ,  0.7963446 ,  3.250815  ,  4.6577425 ,  3.8594632 ,
                   0.39367265,  0.94611126,  0.6230297 ,  0.35022599,  3.6903803 ,
                   2.337941  ,  5.383348  , 12.14523   ,  1.4398934 ,  2.1742728 ,
                   1.6072241 ,  5.467194  ,  1.2596793 ,  2.1560652 ,  1.1517068 ,
                   5.9963036 ,  1.9717857 ,  1.7716382 ,  1.9160262 ,  2.8552551 ,
                   4.745581  ,  7.348962  ,  3.2277074 ,  2.984302  ,  2.2140386 ,
                   1.8019764 ,  0.59824824,  1.8449849 ,  3.216473  ,  6.51493   ,
                   3.411695  ,  7.4430933 ,  6.659884  ,  5.054224  ,  1.388572  ,
                   4.7616067 ,  3.9080114 ,  4.5838494 , 20.273996  ,  3.7882788 ,
                   6.1818533 ,  1.1102964 ,  1.5883152 ,  0.45917422,  8.478489  ,
                   0.09718665,  2.6336462 ,  7.2664666 ,  2.434935  ,  2.8858519 ,
                   0.71751714,  3.0329962 ,  6.130552  ,  0.860823  ,  0.25771728,
                   0.42584717,  0.5142102 ,  0.8449509 ,  4.968134  ,  3.1147995 ,
                   2.4746912 ,  2.0156538 ,  3.6191094 ,  1.2793202 ,  0.7103939 ,
                   3.7820547 ,  6.9056473 ,  4.0495677 ,  1.7817774 ,  2.3426752 ,
                   4.633561  ,  2.070319  ,  1.5363076 ,  0.95820147,  3.6127422 ,
                   0.3730284 ,  0.28459108,  1.723181  ,  4.1297984 ,  2.3784215 ,
                   2.6407814 ,  4.4255576 ,  3.8354557 ,  3.4539526 ,  0.68732715,
                  12.028891  ,  2.09528   ,  3.4303656 ,  3.6795819 ,  2.233653  ,
                   9.531067  ,  2.4739041 ,  1.3033855 ,  1.8244535 ,  2.7561784 ,
                   3.35038   ,  2.4797575 ,  1.2056069 ,  1.42102   ,  3.5945454 ,
                   1.5078974 ,  1.030959  ,  2.032822  ,  1.9084902 ,  0.71502614,
                   0.24140915,  1.3988683 ,  2.2474515 ,  5.052353  ,  0.88052756,
                   3.1064644 ,  5.4538717 ,  0.08182631,  2.2336638 ,  5.490027  ,
                   3.8521888 ,  1.7020229 ,  0.31675732,  0.54662824,  0.5233591 ,
                   7.528719  ,  0.5788549 ,  2.3658106 ,  7.823274  ,  9.688509  ,
                   5.4737873 ,  2.0360384 ,  8.556991  ,  1.9897192 ,  1.9756216 ,
                   4.789227  ,  2.9638944 ,  3.9432104 ,  4.5745883 ,  2.8481593 ,
                   2.703546  ,  0.4868355 ,  0.81143165, 11.803428  ,  2.3433266 ,
                   7.462632  ,  3.5330765 ,  1.769893  ,  3.4632206 ,  6.0739894 ,
                   2.1918657 ,  3.4950104 ,  3.3037906 ,  1.5210805 ,  3.043605  ,
                   4.5550523 ,  1.3057604 ,  2.3426685 ,  0.89967585,  1.4859152 ,
                   0.45666224,  0.29178444,  7.5672245 ,  1.3531511 ,  1.6870949 ],
                 [ 0.9909044 ,  1.5977436 ,  1.5915296 ,  2.5393262 ,  2.087789  ,
                   4.243172  ,  7.001409  ,  9.290381  ,  0.91922265,  7.900055  ,
                   7.7129283 ,  0.6525277 ,  6.4433904 ,  8.98685   ,  3.415953  ,
                   4.779433  ,  4.0793686 ,  7.4854875 ,  1.1678308 ,  4.129944  ,
                   3.0361595 ,  2.4230134 ,  1.9914376 ,  2.428689  ,  2.7493334 ,
                   4.6773024 ,  3.6110651 ,  1.139311  ,  1.1700116 ,  1.7576461 ,
                   4.4287186 ,  1.3367376 ,  1.6895905 ,  6.6807804 ,  3.783243  ,
                   6.1245394 ,  3.9788265 , 13.16905   , 13.16905   , 15.664255  ,
                  15.664255  ,  2.3494203 ,  7.6555758 ,  2.4532216 ,  0.5315145 ,
                   8.000637  ,  3.0699728 ,  1.4240437 ,  3.2925067 ,  2.53016   ,
                   5.606144  ,  1.4063253 ,  4.0349874 ,  5.277519  ,  9.044592  ,
                   3.3025165 ,  6.7250423 ,  4.524832  ,  1.3821722 ,  6.007044  ,
                   2.626573  ,  0.5769744 ,  8.237151  ,  8.070817  ,  1.7475601 ,
                   1.1638703 ,  3.0113087 ,  2.7498362 ,  5.914818  ,  6.1232486 ,
                   0.29810682,  5.1201816 ,  0.563086  ,  1.8486384 ,  4.001296  ,
                   1.2235026 ,  1.8340818 ,  7.513959  ,  0.7324949 ,  2.7174852 ,
                   5.1975183 ,  2.0456045 ,  4.820118  ,  5.1033993 ,  5.1648126 ,
                   3.173502  ,  2.104412  ,  1.9142842 , 11.029547  ,  0.78433573,
                   1.357436  ,  3.3496656 ,  1.1371782 ,  5.2250524 ,  2.2853363 ,
                   1.2432598 ,  2.9474394 ,  2.2762651 , 11.131979  ,  0.03542077,
                   0.09264842,  0.6235244 ,  3.4893827 ,  2.3070836 ,  0.25985214,
                   0.22785841,  0.39597985,  1.5273579 ,  1.6996378 ,  2.936499  ,
                   4.2797337 ,  1.6371739 ,  4.6433635 ,  0.43203235,  0.7139715 ,
                   4.613933  ,  0.9789104 ,  0.0981968 ,  0.53859735,  0.4859575 ,
                   6.3171396 ,  1.0921121 ,  1.5136721 ,  1.112587  ,  2.716591  ,
                   2.309645  ,  0.57045245,  6.38959   ,  4.577489  ,  1.3076562 ,
                   1.4818728 , 13.748591  ,  1.4261547 ,  4.716801  ,  2.5566208 ,
                   3.2431536 ,  2.4402661 ,  0.07903078,  1.96319   ,  3.2732992 ,
                   1.5368414 ,  0.45010495,  0.19129893, 16.928976  ,  0.5482865 ,
                   8.09678   ,  2.225882  ,  3.1512907 ,  4.057416  ,  2.610217  ,
                   2.1332395 ,  9.60669   ,  2.2393262 ,  2.651483  ,  3.3116841 ,
                   1.6829383 ,  2.4401853 ,  1.5279691 ,  3.227448  ,  1.6379778 ,
                   2.4299464 ,  2.075777  ,  3.1862235 ,  3.2390447 ,  2.329407  ,
                   2.201795  ,  5.703568  ,  0.40667385,  0.87402445,  3.3419642 ,
                   4.641601  ,  1.6191708 ,  4.8605385 ,  6.7923694 ,  4.4612546 ,
                   0.7880722 ,  3.642695  ,  5.7544723 ,  2.404113  ,  6.683872  ,
                   0.81219465,  1.7379894 ,  1.7376539 ,  5.8059955 ,  4.278271  ,
                   1.2685912 ,  4.5402994 ,  5.0245523 ,  2.5448208 ,  1.2269168 ,
                   1.2570435 ,  0.09639393,  0.41742703,  2.19767   , 11.426054  ,
                   6.1925087 ,  1.6211317 ,  2.6454413 ,  4.8318114 ,  7.5347095 ,
                   4.0129    ,  4.6609755 ,  3.0834131 ,  1.8212253 ,  0.15747103,
                   0.34305257,  0.50059736,  0.20459786,  0.02735537,  0.47397   ,
                   0.05234714,  0.190357  ,  0.5601471 ,  1.4498736 ,  5.3912153 ,
                   3.1650052 ,  2.2476134 ,  1.4172924 ,  3.296812  ,  4.6089897 ,
                   2.8611212 ,  5.402524  ,  4.947583  ,  1.0548209 ,  0.7901154 ,
                   0.9943615 ,  3.0772898 ,  1.2716869 ,  2.432948  ,  3.8804119 ,
                   1.2244211 ,  0.8237403 ,  4.9685516 ,  1.316479  ,  1.0661899 ,
                   0.16147617,  6.15918   ,  2.6841154 ,  1.4046829 ,  1.5815251 ,
                   4.5101395 ,  4.211768  ,  3.2184887 ,  2.2674942 , 11.533861  ,
                   1.5308465 ,  1.5567675 ,  3.4679332 ,  0.9563234 ,  2.6597273 ,
                   4.113006  ,  5.94164   ,  4.1099057 ,  0.7565336 ,  9.429806  ,
                   2.4552286 ,  0.53369445,  3.3575032 ,  4.5981975 ,  0.05409329,
                   2.4364839 ,  1.5215359 ,  2.9032164 ,  1.1249074 ,  1.1532617 ,
                  19.157143  , 19.157143  ,  1.3512957 ,  0.65963423,  1.5522751 ,
                   0.5923748 , 14.26093   ,  2.619348  ,  7.663063  ,  1.520335  ,
                   1.7601604 ,  4.5279403 ,  5.6468053 ,  2.8692524 ,  1.6483278 ,
                   5.082613  ,  3.348174  ,  7.963322  ,  5.7132883 ,  7.863322  ,
                   1.2458255 ,  2.605769  , 11.989439  ,  0.9381594 ,  1.8971261 ,
                   2.5842643 ,  2.3395038 ,  4.5372963 ,  2.8475537 ,  2.8704324 ,
                   0.7754769 ,  1.4568441 ,  1.3712978 ,  2.1131537 ,  1.5345919 ,
                   0.9531036 ,  0.7739705 ,  1.5121455 ,  9.828634  ,  7.4287105 ,
                   2.9388795 ,  0.2816141 ,  2.3579755 ,  0.14984295,  0.24800135,
                   0.15856981,  1.0296572 ,  2.5968904 ,  7.6706834 ,  0.50782156,
                   8.095074  ,  8.709511  ,  0.73007673,  3.476412  ,  3.0747168 ,
                   1.3265907 ,  0.31783798,  5.4608517 ,  1.749261  ,  1.7294059 ,
                   1.438313  ,  3.280551  ,  0.24643764,  0.66403604,  1.1227971 ,
                   3.8661366 ,  2.7161083 ,  3.560833  ,  4.763618  ,  1.1688248 ,
                   2.1935544 ,  3.8671257 ,  2.203893  ,  1.477727  ,  2.7158074 ,
                   6.5069942 ,  0.456299  ,  1.5456046 ,  4.563259  ,  4.4469385 ,
                   5.397097  ,  5.397097  ,  2.1064    ,  5.4984164 ,  1.3417419 ,
                   1.709095  ,  7.2107835 ,  1.4702858 ,  1.2010643 ,  3.3940632 ,
                   1.6871938 ,  8.092438  ,  1.875149  ,  9.6689    ,  4.6120315 ,
                   3.9952703 ,  1.4235352 ,  8.582107  ,  6.6970954 ,  7.282295  ,
                  14.207127  ,  2.9826918 ,  1.5618287 ,  1.7103666 ,  1.6702276 ,
                   3.8603537 ,  2.7703676 ,  2.6307878 ,  2.504591  , 11.882615  ,
                   3.8029606 , 10.591273  ,  4.6216316 ,  3.2560668 ,  3.2578232 ,
                   3.8841403 ,  8.381626  ,  6.4172707 ,  4.9437313 ,  2.496393  ,
                   2.5616014 ,  5.484207  ,  3.86267   ,  8.52895   ,  1.520958  ,
                   3.0663316 ,  5.64784   ,  0.93371737,  1.988599  ,  3.3644938 ,
                   3.9448767 ,  8.905218  ,  1.6713282 ,  1.7212286 ,  2.0422182 ,
                   3.4921372 ,  3.8627925 ,  0.26233172,  0.43868166,  3.3021283 ,
                   3.651146  ,  3.651146  ,  2.4456723 ,  9.569137  ,  2.3459058 ,
                   0.2361946 ,  2.2865353 , 16.966942  ,  9.5944605 ,  3.9430783 ,
                   7.300621  ,  8.237884  ,  1.1408961 ,  3.106974  ,  5.3557086 ,
                   4.113908  ,  0.73947203,  0.8736652 ,  2.8615105 ,  4.674794  ,
                   1.346915  ,  0.6225802 ,  0.19296533,  6.3390613 ,  2.802343  ,
                   3.9072082 ,  1.5721794 ,  4.805414  ,  0.9118719 ,  6.6454163 ,
                   0.35046232,  8.147577  ,  5.0826526 ,  3.0514736 ,  1.8530624 ,
                   1.573253  ,  2.814517  ,  3.2968137 ,  3.1585622 ,  2.970489  ,
                   4.581018  ,  1.5554717 ,  0.6137824 ,  2.1317117 ,  5.246378  ,
                   4.361018  ,  2.8805962 ,  2.4948945 ,  6.1967874 ,  0.5377769 ,
                   0.37031844,  0.7325885 ,  1.9997089 ,  2.398744  ,  2.0033321 ,
                   1.6943733 ,  5.4950047 ,  5.6807523 ,  2.5063794 ,  3.8039002 ,
                  11.003864  ,  0.7521229 ,  7.85719   ,  1.0913641 ,  2.1949823 ,
                   8.510656  ,  3.865408  ,  2.2440512 ,  4.94407   , 13.895223  ,
                   0.26907384,  1.5775707 ,  2.8049283 ,  1.0583861 ,  1.3993121 ,
                   2.1294248 ,  3.9265387 ,  3.4271214 ,  1.6736029 ,  2.3646955 ,
                   0.47015515,  4.9279428 ,  3.7552726 ,  3.7249236 ,  1.6924706 ,
                   0.331155  ,  2.1292431 ,  0.959191  ,  2.2490025 ,  9.622374  ,
                   5.5982914 ,  4.0080676 ,  2.5344353 ,  2.7411196 ,  4.101541  ]],
                dtype=float32)
        • theta_tilde
          (chain, draw, theta_tilde_dim_0)
          float32
          0.6061655 1.8185308 ... -1.4317532
          array([[[ 0.6061655 ,  1.8185308 , -0.09561205, ..., -1.3342378 ,
                    0.70666367,  0.04662064],
                  [ 1.0919316 ,  0.7878127 ,  0.51768357, ..., -0.86000085,
                    1.1659694 ,  1.070951  ],
                  [-0.44649038, -1.1334856 , -0.08350085, ..., -0.79331404,
                    0.80516696,  0.05294776],
                  ...,
                  [ 0.27960604, -0.6067694 ,  0.63655376, ...,  1.3932375 ,
                   -0.6413138 , -0.09322856],
                  [ 0.65896815,  1.2729853 , -0.16130266, ...,  0.538792  ,
                    2.0496454 ,  0.28260455],
                  [ 0.6073655 ,  0.49289384,  0.3575558 , ..., -0.46220857,
                    0.6597414 ,  1.7932637 ]],
          
                 [[-0.05533975,  1.5325787 , -0.02127528, ..., -0.8900326 ,
                   -0.39435595, -0.55493706],
                  [ 1.0245105 ,  1.0371798 , -0.12512936, ...,  1.3573611 ,
                    0.12283397,  0.33178735],
                  [ 1.2065461 ,  0.14588034, -0.02969379, ...,  0.61200786,
                   -0.50436723,  0.29426408],
                  ...,
                  [ 0.5336305 , -0.36422867,  0.607937  , ..., -0.33750185,
                    0.75881875, -0.354092  ],
                  [ 0.11554712, -0.7284259 ,  1.029543  , ..., -0.9233731 ,
                    0.17342997,  0.47577518],
                  [-0.5292633 ,  0.8391605 , -1.8189237 , ..., -0.04487276,
                    1.7539048 , -1.4317532 ]]], dtype=float32)
      • created_at :
        2020-06-10T18:21:33.589496
        arviz_version :
        0.8.3
        inference_library :
        pyro
        inference_library_version :
        1.1.0

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 2
        • draw: 500
        • obs_dim_0: 8
        • chain
          (chain)
          int64
          0 1
          array([0, 1])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 495 496 497 498 499
          array([  0,   1,   2, ..., 497, 498, 499])
        • obs_dim_0
          (obs_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • obs
          (chain, draw, obs_dim_0)
          float32
          17.056637 13.765715 ... -33.684814
          array([[[ 17.056637  ,  13.765715  ,  28.1891    , ...,  11.842781  ,
                    11.978273  ,   0.3044815 ],
                  [ 21.057343  ,  -7.351166  ,  11.830295  , ...,  -5.1788282 ,
                    11.68743   ,  22.859253  ],
                  [  7.56715   ,   6.8423553 ,   5.7562637 , ...,   3.304874  ,
                     5.348268  ,  16.123114  ],
                  ...,
                  [ 32.053898  ,  -9.957651  ,  -0.8588064 , ...,   7.980326  ,
                     3.5410204 , -14.456598  ],
                  [ 20.119667  ,  -7.6601057 ,  -2.9862726 , ...,  -0.10599685,
                     1.5778246 , -16.948988  ],
                  [ 25.463974  , -14.382548  ,  19.056568  , ..., -14.948351  ,
                   -15.824716  ,   7.1326447 ]],
          
                 [[ -4.4520526 ,   3.186278  ,   4.188992  , ...,   1.6511054 ,
                     8.9940605 ,   1.2203226 ],
                  [ 23.332848  ,  13.669164  ,  -0.15677023, ...,  -6.408621  ,
                    22.05013   ,   1.6746373 ],
                  [ 29.850473  ,   0.35601377,  31.621748  , ...,  24.21464   ,
                     8.574121  ,  -4.5073214 ],
                  ...,
                  [ 10.046104  ,  -9.08149   ,  24.914795  , ...,   0.8853679 ,
                    -3.557653  ,   1.4098097 ],
                  [-16.446758  ,  21.567833  ,  17.841633  , ...,  11.072165  ,
                    19.724937  ,  -5.2535686 ],
                  [ -4.726616  ,   4.298817  ,  10.874061  , ...,   0.40810192,
                     5.026056  , -33.684814  ]]], dtype=float32)
      • created_at :
        2020-06-10T18:21:33.925982
        arviz_version :
        0.8.3
        inference_library :
        pyro
        inference_library_version :
        1.1.0

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 2
        • draw: 500
        • obs_dim_0: 8
        • chain
          (chain)
          int64
          0 1
          array([0, 1])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 495 496 497 498 499
          array([  0,   1,   2, ..., 497, 498, 499])
        • obs_dim_0
          (obs_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • obs
          (chain, draw, obs_dim_0)
          float32
          -4.4705133 -3.3008652 ... -4.252307
          array([[[-4.4705133, -3.3008652, -3.8681855, ..., -3.3328528,
                   -3.6443205, -3.8491797],
                  [-4.2400713, -3.22724  , -3.8871422, ..., -3.4007401,
                   -3.404223 , -3.810225 ],
                  [-5.572689 , -3.8407664, -3.70118  , ..., -3.3636737,
                   -4.6304407, -4.0493298],
                  ...,
                  [-5.2727504, -4.190528 , -3.773724 , ..., -3.5955849,
                   -6.145524 , -4.1133003],
                  [-4.9237747, -3.276835 , -3.7557254, ..., -3.3465247,
                   -3.9749088, -3.925208 ],
                  [-5.274494 , -3.4969072, -3.71345  , ..., -3.333908 ,
                   -4.6904016, -3.9407105]],
          
                 [[-4.806156 , -3.2322083, -3.8164787, ..., -3.3575134,
                   -4.1154737, -3.89682  ],
                  [-4.472113 , -3.2228694, -3.8738499, ..., -3.5833087,
                   -3.8201694, -3.8420815],
                  [-4.4680734, -3.228054 , -3.8706927, ..., -3.4967794,
                   -3.9630103, -3.8464642],
                  ...,
                  [-5.3380413, -3.7239227, -3.7146387, ..., -3.3529468,
                   -4.696886 , -4.111705 ],
                  [-4.487238 , -3.2412963, -4.0651107, ..., -3.3996596,
                   -3.6743426, -3.8204584],
                  [-5.527108 , -3.2873592, -3.7158775, ..., -3.3171015,
                   -3.709279 , -4.252307 ]]], dtype=float32)
      • created_at :
        2020-06-10T18:21:33.876187
        arviz_version :
        0.8.3
        inference_library :
        pyro
        inference_library_version :
        1.1.0

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 2
        • draw: 500
        • chain
          (chain)
          int64
          0 1
          array([0, 1])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 495 496 497 498 499
          array([  0,   1,   2, ..., 497, 498, 499])
        • diverging
          (chain, draw)
          bool
          False False False ... False False
          array([[False, False, False, False, False, False, False, False, False,
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                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
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                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
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                  False, False, False, False, False, False, False, False, False,
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                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
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                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False],
                 [False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
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                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
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                  False, False, False, False, False, False, False, False, False,
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                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
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                  False, False, False, False, False, False, False, False, False,
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                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False]])
      • created_at :
        2020-06-10T18:21:33.823431
        arviz_version :
        0.8.3
        inference_library :
        pyro
        inference_library_version :
        1.1.0

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 1
        • draw: 500
        • theta_tilde_dim_0: 8
        • chain
          (chain)
          int64
          0
          array([0])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 495 496 497 498 499
          array([  0,   1,   2, ..., 497, 498, 499])
        • theta_tilde_dim_0
          (theta_tilde_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • mu
          (chain, draw)
          float32
          1.8310521 7.369206 ... -0.07544144
          array([[ 1.83105206e+00,  7.36920595e+00, -1.19266405e+01,
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                  -1.86073518e+00,  6.28713250e-01,  6.81693649e+00,
                   7.71915436e+00,  7.51500702e+00,  6.99194527e+00,
                   6.81107426e+00, -6.58409548e+00, -8.57430363e+00,
                   8.83453548e-01,  6.32625198e+00, -2.42169404e+00,
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                  -2.45449328e+00,  6.48085117e+00,  1.84746668e-01,
                   9.50277996e+00,  1.59419513e+00, -7.20801449e+00,
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                   4.47114372e+00, -3.56763458e+00, -4.17484492e-01,
                   2.15950990e+00,  1.10670459e+00, -4.33139133e+00,
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                  -2.73538065e+00,  2.09568596e+00,  4.75485802e+00,
                   1.26565361e+00,  5.04449546e-01, -4.07291603e+00,
                   5.41869581e-01,  4.77750123e-01, -1.77831125e+00,
                  -2.42855740e+00,  5.80212212e+00,  2.78317261e+00,
                  -8.38098049e-01, -1.13215065e+01,  1.04781361e+01,
                  -1.98796690e-02, -8.12773609e+00,  3.65236521e+00,
                   4.78217268e+00,  5.68206692e+00,  1.17952776e+00,
                   3.48964882e+00, -7.54414424e-02]], dtype=float32)
        • tau
          (chain, draw)
          float32
          233.58215 994.4366 ... 27.182827
          array([[2.33582153e+02, 9.94436584e+02, 2.88996196e+00, 4.46266115e-01,
                  4.96314669e+00, 5.80443611e+01, 6.78751850e+00, 1.49578667e+00,
                  7.38433151e+01, 4.20371771e+00, 3.13775492e+00, 8.71614647e+00,
                  3.26564932e+00, 4.71219480e-01, 3.88621855e+00, 5.17096996e+00,
                  6.44069195e+00, 2.11158514e+00, 8.10319036e-02, 4.32135868e+00,
                  3.56079245e+00, 7.56645775e+00, 3.47996688e+00, 8.96701574e-01,
                  8.81987810e-01, 6.37050915e+00, 1.29537487e+00, 2.42891556e+02,
                  1.45000434e+00, 3.44764090e+00, 4.36339569e+00, 6.93003559e+00,
                  1.21201019e+01, 1.22789011e+01, 6.61703014e+00, 3.75274944e+00,
                  4.36765718e+00, 1.34682770e+01, 4.79594326e+00, 6.00994720e+01,
                  2.38157487e+00, 8.64460068e+01, 1.70366192e+00, 3.13302803e+00,
                  1.08464298e+01, 1.89743690e+01, 1.00153017e+01, 4.93525600e+00,
                  2.10727382e+00, 2.61057854e+00, 4.94686413e+00, 2.40696449e+01,
                  2.96104956e+00, 1.18571396e+01, 2.97007084e+01, 6.49375916e+00,
                  5.76199579e+00, 9.28328037e+00, 2.05416012e+00, 4.67196894e+00,
                  1.94539279e-01, 1.69849586e+00, 4.11854172e+00, 9.30481796e+01,
                  1.30114019e+00, 6.92282200e+00, 2.10049458e+01, 1.03697910e+01,
                  1.64222889e+01, 7.37519503e-01, 8.64608002e+00, 1.58246374e+00,
                  1.15422897e+01, 1.25697498e+01, 2.78301773e+01, 2.34611492e+01,
                  4.61381073e+01, 8.49647427e+00, 2.38395095e+00, 3.06760292e+01,
                  8.38161111e-01, 8.70039749e+00, 3.20347100e-01, 2.86008606e+01,
                  6.00329304e+00, 1.99586225e+00, 1.01666679e+01, 8.67040217e-01,
                  1.96274054e+00, 8.22034546e+02, 3.25686569e+01, 7.47367191e+00,
                  5.82090683e+01, 6.80117130e-01, 1.32837164e+00, 2.87984238e+01,
                  2.78351212e+00, 6.56047773e+00, 7.62254834e-01, 1.19701965e+02,
                  3.16393661e+00, 9.53789806e+00, 1.14697514e+01, 9.03164291e+00,
                  1.99453759e+00, 5.68666697e+00, 1.65687599e+01, 1.67806506e-01,
                  7.41473317e-01, 3.13937008e-01, 2.65185714e+00, 3.46124039e+01,
                  1.43749255e+03, 4.64936829e+00, 1.42269874e+00, 3.32906990e+01,
                  1.39783907e+00, 1.89604580e+00, 6.28229370e+01, 4.18284950e+01,
                  7.72986352e-01, 2.69628406e+00, 2.78242207e+00, 2.73950160e-01,
                  5.61358929e+00, 3.10696411e+00, 4.68212414e+00, 1.69084892e-01,
                  1.76831853e+00, 3.58425570e+00, 1.66552944e+01, 6.66814518e+00,
                  2.22552757e+01, 2.18585186e+01, 4.84984636e+00, 2.61942062e+01,
                  6.71889210e+00, 3.07793331e+01, 7.65414143e+00, 6.03538275e+00,
                  1.08152752e+01, 1.53035221e+01, 1.82176857e+01, 5.10415316e+00,
                  2.33483219e+01, 9.00594652e-01, 1.42888498e+01, 1.11383905e+01,
                  2.80002928e+00, 1.97191668e+00, 9.47514629e+00, 1.59550037e+01,
                  1.24129760e+00, 3.00389910e+00, 7.33918142e+00, 2.03434730e+00,
                  1.40971959e+00, 2.60195613e+00, 5.19892263e+00, 4.85553789e+00,
                  4.01490164e+00, 5.50108337e+00, 1.95370235e+01, 3.57205272e+00,
                  3.22123230e-01, 3.18224182e+01, 5.46338511e+00, 3.92666698e+00,
                  1.19204788e+01, 3.34672689e+00, 1.28777447e+01, 7.79884398e-01,
                  6.61139846e-01, 1.53919148e+00, 2.90023565e+00, 2.00248814e+00,
                  5.53505516e+00, 6.83246183e+00, 4.38924694e+00, 8.34967804e+00,
                  5.10579491e+00, 1.58182859e+01, 1.78390675e+01, 5.87143898e+00,
                  8.79881096e+00, 2.89170361e+00, 1.12620888e+01, 1.57768428e+00,
                  2.32329521e+01, 5.88128757e+00, 3.41677904e+00, 7.61884537e+01,
                  5.26621222e-01, 2.92264342e+00, 1.46880138e+00, 1.58016682e+00,
                  3.81652985e+01, 2.46611953e+00, 4.79778290e+00, 1.88320708e+00,
                  1.90092564e+00, 7.12588310e-01, 9.07944775e+00, 7.06309557e+00,
                  2.61442447e+00, 1.78211820e+00, 3.95346403e+00, 2.53750610e+00,
                  8.14840674e-01, 2.00210166e+00, 2.62024078e+01, 5.12925744e-01,
                  6.95824099e+00, 2.35959935e+00, 1.71262836e+00, 5.10069351e+01,
                  3.19263029e+00, 1.15136087e-01, 1.57397881e+01, 9.10933018e-01,
                  2.54393845e+01, 1.22716546e+00, 6.51532364e+00, 2.91248016e+01,
                  6.27013743e-02, 7.57493925e+00, 1.00060427e+00, 1.94976521e+00,
                  1.05164957e+01, 1.20389929e+01, 7.51705074e+00, 1.34320679e+02,
                  4.60176182e+00, 5.06012535e+00, 3.81312418e+00, 3.13340473e+00,
                  1.12241850e+01, 6.68661475e-01, 9.63961029e+00, 1.80393448e+01,
                  1.27726388e+00, 8.14500600e-02, 1.34037886e+01, 4.43923569e+00,
                  9.86487961e+00, 4.39872217e+00, 4.16832018e+00, 1.09472620e+00,
                  2.91746311e+01, 1.49736700e+01, 9.17174101e-01, 1.25601950e+01,
                  5.54890394e-01, 5.42279053e+00, 1.89136982e+00, 3.33140159e+00,
                  5.18533659e+00, 8.20474243e+00, 3.74159360e+00, 6.61919546e+00,
                  9.13305569e+00, 1.16696537e+00, 6.32780876e+01, 4.78538799e+00,
                  9.15983295e+00, 1.19233716e+00, 4.15419197e+00, 3.01625061e+00,
                  1.33225393e+01, 8.89955699e-01, 3.94315934e+00, 1.25022098e-01,
                  1.56112921e+00, 2.40924430e+00, 5.45164061e+00, 3.19068031e+01,
                  2.74245787e+00, 5.39334259e+01, 2.68976002e+01, 3.05201454e+01,
                  1.01681805e+00, 3.24505115e+00, 3.51270258e-01, 3.39455485e+00,
                  1.03448999e+00, 6.52295971e+00, 8.54770851e+00, 3.17444348e+00,
                  1.41029816e+01, 8.06216145e+00, 4.02719927e+00, 8.40551949e+00,
                  7.55664349e+00, 5.41498232e+00, 2.03295345e+01, 1.33403766e+00,
                  3.10369968e+00, 9.22239971e+00, 1.33640230e+00, 3.04194498e+00,
                  1.49802998e-01, 7.67462845e+01, 1.00229049e+00, 9.41823196e+00,
                  2.40813103e+01, 5.96192837e-01, 1.24422464e+01, 6.29803009e+01,
                  9.61070156e+00, 3.14717960e+00, 3.35008736e+01, 1.62203751e+02,
                  4.78771782e+00, 9.57639408e+00, 2.18938899e+00, 6.93462944e+00,
                  1.47582645e+01, 1.59039507e+01, 3.55825844e+01, 1.57970297e+00,
                  6.86061192e+00, 1.46212173e+00, 1.21917558e+00, 5.43149567e+00,
                  1.26152265e+00, 2.14529729e+00, 3.60484076e+00, 3.20548248e+00,
                  8.68775845e+00, 4.69007778e+00, 6.97661924e+00, 2.86727786e+00,
                  6.55940008e+00, 3.04591227e+00, 6.40091038e+00, 7.69913483e+01,
                  1.76605213e+00, 1.69695389e+00, 1.49314392e+02, 1.74520826e+00,
                  2.10937786e+00, 1.85648233e-01, 7.94631481e+00, 4.20290565e+00,
                  1.58578515e+00, 2.86422396e+00, 2.78503656e+00, 1.90926838e+01,
                  2.03964019e+00, 2.16318626e+01, 9.85763626e+01, 8.25113773e+00,
                  7.35772908e-01, 4.36113882e+00, 1.37380188e+02, 4.84867334e+00,
                  1.83547437e+00, 7.29557495e+01, 1.18845024e+01, 6.21232643e+01,
                  8.89026070e+00, 8.67310905e+00, 9.10755172e-02, 4.66671085e+00,
                  7.80379639e+01, 4.44808617e+01, 1.78106499e+01, 1.36136341e+01,
                  1.11453638e+01, 6.47962141e+00, 3.14819312e+00, 3.80757451e+00,
                  6.99266315e-01, 5.32106857e+01, 2.26561832e+00, 1.17912173e+00,
                  1.61539803e+01, 1.64006214e+01, 6.56036139e+00, 2.02290916e+01,
                  1.35110483e+01, 1.61717999e+00, 4.25558233e+00, 1.24771166e+00,
                  8.42467189e-01, 3.71366239e+00, 1.12391367e+01, 7.85699415e+00,
                  1.17313776e+01, 2.07943416e+00, 1.07938728e+01, 1.71249676e+01,
                  4.25358963e+00, 3.37078810e+00, 2.89949465e+00, 6.30591965e+01,
                  8.41671944e-01, 2.24199390e+00, 2.29184461e+00, 1.12583256e+01,
                  1.59082878e+00, 1.61483455e+00, 8.51412296e+00, 2.94279718e+00,
                  1.55814886e+00, 1.94127309e+00, 3.83025789e+00, 7.02682590e+00,
                  2.06390142e+00, 1.34827960e+00, 2.81168457e+02, 6.22805953e-01,
                  8.24851453e-01, 2.11877942e-01, 3.92178574e+01, 9.66570312e+02,
                  3.94462729e+00, 7.99840927e-01, 1.70189846e+00, 1.00781441e+01,
                  2.87433743e-01, 1.20128322e+00, 2.29061928e+01, 3.59614491e+00,
                  4.05278158e+00, 1.58789263e+01, 1.11763752e+00, 1.74107971e+01,
                  1.57513487e+00, 1.86496060e-02, 7.02734985e+01, 3.25848503e+01,
                  3.71071362e+00, 1.89383469e+01, 4.06730556e+00, 1.25093555e+00,
                  1.31658208e+00, 6.87853718e+00, 4.67559671e+00, 2.59621410e+01,
                  2.93781424e+00, 8.28132534e+00, 2.93957710e+00, 2.71064987e+01,
                  1.96016669e-01, 7.85356760e-01, 3.60274577e+00, 2.52142549e+00,
                  6.00418663e+00, 1.30085669e+01, 4.41197300e+00, 4.23312283e+00,
                  1.43678570e+00, 9.44298446e-01, 1.23984262e-01, 4.08745956e+01,
                  3.59652996e-01, 4.51054305e-01, 2.02281017e+01, 5.19320641e+01,
                  2.71144605e+00, 2.10441933e+01, 2.76381893e+01, 2.75218344e+00,
                  1.07174101e+01, 1.65728331e+00, 1.40117636e+01, 5.70923004e+01,
                  2.04354548e+00, 7.14082837e-01, 1.98984873e+00, 2.52286911e+01,
                  2.85708785e+00, 8.33650780e+00, 3.08708382e+00, 4.20598221e+00,
                  3.83560791e+01, 6.60561275e+00, 3.31780434e+00, 1.28404593e+00,
                  1.66767464e+01, 6.89008808e+00, 5.83668041e+00, 1.42359662e+00,
                  6.85395598e-02, 9.49191093e-01, 1.09593658e+01, 1.75060701e+00,
                  1.01909657e+01, 4.41580963e+00, 1.00245590e+01, 8.76809508e-02,
                  5.11244965e+00, 3.84632111e+00, 7.63232660e+00, 4.04119635e+00,
                  2.86264753e+00, 5.07223177e+00, 9.76756382e+00, 2.71828270e+01]],
                dtype=float32)
        • theta_tilde
          (chain, draw, theta_tilde_dim_0)
          float32
          0.6022393 ... -0.31073767
          array([[[ 0.6022393 , -0.39827886,  0.19862896, ..., -0.95424646,
                   -1.1647658 ,  0.3821102 ],
                  [-1.497994  ,  0.74775034, -0.78757095, ..., -1.6560527 ,
                   -1.613713  , -0.46137986],
                  [-0.16146933,  0.2763805 , -0.8783446 , ...,  0.56389153,
                   -0.01581344, -0.8957549 ],
                  ...,
                  [-1.1428025 , -1.1540538 , -1.0932158 , ...,  1.6082281 ,
                   -2.009276  , -0.5227252 ],
                  [ 1.8399812 ,  0.33280653,  0.45785332, ...,  1.834717  ,
                    0.8924277 ,  1.2369446 ],
                  [-0.14975677,  0.8303282 , -0.00824529, ..., -1.6754906 ,
                    0.26279444, -0.31073767]]], dtype=float32)
      • created_at :
        2020-06-10T18:21:33.976125
        arviz_version :
        0.8.3
        inference_library :
        pyro
        inference_library_version :
        1.1.0

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 1
        • draw: 500
        • obs_dim_0: 8
        • chain
          (chain)
          int64
          0
          array([0])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 495 496 497 498 499
          array([  0,   1,   2, ..., 497, 498, 499])
        • obs_dim_0
          (obs_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • obs
          (chain, draw, obs_dim_0)
          float32
          152.4126 -104.43863 ... -19.538307
          array([[[ 1.5241260e+02, -1.0443863e+02,  5.3149067e+01, ...,
                   -2.1432968e+02, -2.7346640e+02,  9.8980553e+01],
                  [-1.4595604e+03,  7.5740137e+02, -7.9331067e+02, ...,
                   -1.6279233e+03, -1.6046724e+03, -4.5491840e+02],
                  [-1.2688635e+01, -1.5242083e+01,  6.5625114e+00, ...,
                    7.7777863e-01,  1.3528487e+01, -4.4868240e+01],
                  ...,
                  [ 6.5915680e+00, -8.9369183e+00, -1.1899769e+01, ...,
                   -1.4138508e-01, -2.4801119e+01, -1.1125523e+00],
                  [ 1.1234647e+01,  9.1552639e+00,  1.3359819e+01, ...,
                    6.3331509e+00, -6.9926414e+00,  2.9034739e+01],
                  [ 3.9082799e+00,  2.4938337e+01,  1.8535004e+01, ...,
                   -4.8968292e+01,  1.1919480e+01, -1.9538307e+01]]], dtype=float32)
      • created_at :
        2020-06-10T18:21:34.025492
        arviz_version :
        0.8.3
        inference_library :
        pyro
        inference_library_version :
        1.1.0

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • obs_dim_0: 8
        • obs_dim_0
          (obs_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • obs
          (obs_dim_0)
          float32
          28.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
          array([28.,  8., -3.,  7., -1.,  1., 18., 12.], dtype=float32)
      • created_at :
        2020-06-10T18:21:34.070465
        arviz_version :
        0.8.3
        inference_library :
        pyro
        inference_library_version :
        1.1.0

From emcee

[10]:
import emcee

eight_school_data = {
    "J": 8,
    "y": np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
    "sigma": np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}


def log_prior_8school(theta, J):
    mu = theta[0]
    tau = theta[1]
    eta = theta[2:]
    # Half-cauchy prior
    if tau < 0:
        return -np.inf
    hwhm = 25
    prior_tau = -np.log(tau ** 2 + hwhm ** 2)
    prior_mu = -((mu / 10) ** 2)  # normal prior, loc=0, scale=10
    prior_eta = -np.sum(eta ** 2)  # normal prior, loc=0, scale=1
    return prior_mu + prior_tau + prior_eta


def log_likelihood_8school(theta, y, sigma):
    mu = theta[0]
    tau = theta[1]
    eta = theta[2:]
    return -np.sum(((mu + tau * eta - y) / sigma) ** 2)


def lnprob_8school(theta, J, y, sigma):
    prior = log_prior_8school(theta, J)
    if prior <= -np.inf:
        return -np.inf
    like = log_likelihood_8school(theta, y, sigma)
    return like + prior


nwalkers = 40
ndim = eight_school_data["J"] + 2
draws = 1500
pos = np.random.normal(size=(nwalkers, ndim))
pos[:, 1] = np.absolute(pos[:, 1])
sampler = emcee.EnsembleSampler(
    nwalkers,
    ndim,
    lnprob_8school,
    args=(eight_school_data["J"], eight_school_data["y"], eight_school_data["sigma"]),
)
sampler.run_mcmc(pos, draws)

# define variable names, it cannot be inferred from emcee
var_names = ["mu", "tau"] + ["eta{}".format(i) for i in range(eight_school_data["J"])]
emcee_data = az.from_emcee(sampler, var_names=var_names)
emcee_data
[10]:
arviz.InferenceData
    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 40
        • draw: 1500
        • chain
          (chain)
          int64
          0 1 2 3 4 5 6 ... 34 35 36 37 38 39
          array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
                 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
                 36, 37, 38, 39])
        • draw
          (draw)
          int64
          0 1 2 3 4 ... 1496 1497 1498 1499
          array([   0,    1,    2, ..., 1497, 1498, 1499])
        • mu
          (chain, draw)
          float64
          0.9284 0.7497 ... -1.109 -1.109
          array([[ 0.92841914,  0.74969441,  0.74969441, ...,  4.72566447,
                   4.72221834,  4.72221834],
                 [ 0.04751325,  0.04751325,  0.04751325, ...,  6.30209019,
                   6.30209019,  6.30209019],
                 [-2.55298982, -2.55298982, -2.55298982, ...,  9.28990943,
                   9.28990943,  7.96917791],
                 ...,
                 [ 0.75359111,  0.75359111,  0.75359111, ...,  0.62855896,
                   0.62855896,  0.62855896],
                 [-1.64097945, -1.64097945, -1.41262278, ...,  4.42408698,
                   4.60329133,  3.89910876],
                 [ 0.56729028,  0.56729028,  0.56729028, ..., -1.10909274,
                  -1.10909274, -1.10909274]])
        • tau
          (chain, draw)
          float64
          0.7789 0.9465 ... 8.763 8.763
          array([[ 0.77890285,  0.94646991,  0.94646991, ...,  3.06241616,
                   3.06435583,  3.06435583],
                 [ 1.32485136,  1.32485136,  1.32485136, ...,  0.74095528,
                   0.74095528,  0.74095528],
                 [ 0.6536186 ,  0.6536186 ,  0.6536186 , ...,  0.57241746,
                   0.57241746,  3.8804493 ],
                 ...,
                 [ 0.93276919,  0.93276919,  0.93276919, ..., 20.11266279,
                  20.11266279, 20.11266279],
                 [ 0.37813884,  0.37813884,  0.42137438, ...,  7.74062311,
                   6.91967957,  4.92296393],
                 [ 0.2226751 ,  0.2226751 ,  0.2226751 , ...,  8.76313578,
                   8.76313578,  8.76313578]])
        • eta0
          (chain, draw)
          float64
          0.5965 0.356 ... 0.9787 0.9787
          array([[ 0.59650655,  0.35598681,  0.35598681, ...,  0.71466293,
                   0.71523086,  0.71523086],
                 [ 0.5749315 ,  0.5749315 ,  0.5749315 , ..., -0.12368357,
                  -0.12368357, -0.12368357],
                 [ 0.8644362 ,  0.8644362 ,  0.8644362 , ..., -0.40901378,
                  -0.40901378, -0.06287993],
                 ...,
                 [ 0.82396593,  0.82396593,  0.82396593, ...,  0.77767883,
                   0.77767883,  0.77767883],
                 [-2.17958654, -2.17958654, -2.07240863, ...,  0.26757447,
                   0.3684135 ,  0.23850609],
                 [-0.35343175, -0.35343175, -0.35343175, ...,  0.97868557,
                   0.97868557,  0.97868557]])
        • eta1
          (chain, draw)
          float64
          1.395 0.9969 0.9969 ... 2.189 2.189
          array([[ 1.39536064,  0.99693975,  0.99693975, ..., -0.18711784,
                  -0.18694776, -0.18694776],
                 [-0.0967978 , -0.0967978 , -0.0967978 , ...,  0.59447501,
                   0.59447501,  0.59447501],
                 [-0.74216502, -0.74216502, -0.74216502, ...,  0.50398771,
                   0.50398771,  0.4091619 ],
                 ...,
                 [ 0.08496028,  0.08496028,  0.08496028, ...,  0.35080969,
                   0.35080969,  0.35080969],
                 [-0.99002989, -0.99002989, -0.86249973, ..., -0.71346413,
                  -0.6690839 , -1.30316671],
                 [-1.61647419, -1.61647419, -1.61647419, ...,  2.1885378 ,
                   2.1885378 ,  2.1885378 ]])
        • eta2
          (chain, draw)
          float64
          1.428 1.154 1.154 ... 0.1311 0.1311
          array([[ 1.42788977,  1.15418066,  1.15418066, ...,  1.3167935 ,
                   1.31822332,  1.31822332],
                 [ 0.41236399,  0.41236399,  0.41236399, ..., -0.34438568,
                  -0.34438568, -0.34438568],
                 [ 2.26975462,  2.26975462,  2.26975462, ...,  0.74946974,
                   0.74946974,  0.11741706],
                 ...,
                 [-0.11300394, -0.11300394, -0.11300394, ...,  0.01968209,
                   0.01968209,  0.01968209],
                 [ 0.03733591,  0.03733591, -0.02665422, ...,  0.08855891,
                   0.09957141,  0.873668  ],
                 [-0.29183736, -0.29183736, -0.29183736, ...,  0.13107062,
                   0.13107062,  0.13107062]])
        • eta3
          (chain, draw)
          float64
          -0.7293 -0.7175 ... 0.3588 0.3588
          array([[-0.72926825, -0.71747056, -0.71747056, ..., -0.24082616,
                  -0.24043765, -0.24043765],
                 [ 0.24672591,  0.24672591,  0.24672591, ..., -0.89020229,
                  -0.89020229, -0.89020229],
                 [-1.45436567, -1.45436567, -1.45436567, ..., -1.31071147,
                  -1.31071147, -0.68573358],
                 ...,
                 [ 0.39412955,  0.39412955,  0.39412955, ...,  0.38296835,
                   0.38296835,  0.38296835],
                 [-1.61338832, -1.61338832, -1.39419799, ..., -0.20925129,
                  -0.08789249, -0.44863267],
                 [-0.76149221, -0.76149221, -0.76149221, ...,  0.35875544,
                   0.35875544,  0.35875544]])
        • eta4
          (chain, draw)
          float64
          0.2754 0.428 ... 0.1813 0.1813
          array([[ 0.27536896,  0.42802117,  0.42802117, ..., -0.64697444,
                  -0.647279  , -0.647279  ],
                 [ 1.1247147 ,  1.1247147 ,  1.1247147 , ..., -0.3792712 ,
                  -0.3792712 , -0.3792712 ],
                 [ 0.04575852,  0.04575852,  0.04575852, ..., -0.04265142,
                  -0.04265142, -0.03572373],
                 ...,
                 [ 0.97692625,  0.97692625,  0.97692625, ...,  0.19855731,
                   0.19855731,  0.19855731],
                 [-0.96656389, -0.96656389, -0.92286515, ..., -0.7191441 ,
                  -0.66556347, -1.11350372],
                 [ 0.85792392,  0.85792392,  0.85792392, ...,  0.18125692,
                   0.18125692,  0.18125692]])
        • eta5
          (chain, draw)
          float64
          -0.5001 -0.6041 ... -0.1164 -0.1164
          array([[-0.50013399, -0.60410533, -0.60410533, ..., -1.08707667,
                  -1.08765507, -1.08765507],
                 [-0.12619171, -0.12619171, -0.12619171, ..., -0.30565393,
                  -0.30565393, -0.30565393],
                 [-0.18718385, -0.18718385, -0.18718385, ..., -0.98486991,
                  -0.98486991, -0.44800379],
                 ...,
                 [-2.04134322, -2.04134322, -2.04134322, ...,  0.95433456,
                   0.95433456,  0.95433456],
                 [-1.44616313, -1.44616313, -1.38958095, ...,  0.07653725,
                   0.00765534, -0.34260937],
                 [ 1.14110187,  1.14110187,  1.14110187, ..., -0.11644015,
                  -0.11644015, -0.11644015]])
        • eta6
          (chain, draw)
          float64
          0.1888 -0.05081 ... 0.6959 0.6959
          array([[ 1.88821093e-01, -5.08071132e-02, -5.08071132e-02, ...,
                   2.20885330e-01,  2.21008935e-01,  2.21008935e-01],
                 [ 1.68791224e-01,  1.68791224e-01,  1.68791224e-01, ...,
                  -7.62386375e-01, -7.62386375e-01, -7.62386375e-01],
                 [ 1.53277921e+00,  1.53277921e+00,  1.53277921e+00, ...,
                  -8.44490237e-01, -8.44490237e-01, -3.47285167e-01],
                 ...,
                 [ 1.35927742e-02,  1.35927742e-02,  1.35927742e-02, ...,
                   7.83259115e-01,  7.83259115e-01,  7.83259115e-01],
                 [ 1.60246678e+00,  1.60246678e+00,  1.58314291e+00, ...,
                   1.25047974e-01,  2.21093345e-01, -1.19317876e-03],
                 [ 1.46657872e+00,  1.46657872e+00,  1.46657872e+00, ...,
                   6.95921870e-01,  6.95921870e-01,  6.95921870e-01]])
        • eta7
          (chain, draw)
          float64
          0.2937 0.1625 ... 1.533 1.533
          array([[ 0.29370708,  0.16252705,  0.16252705, ..., -1.50049936,
                  -1.50147066, -1.50147066],
                 [-0.74697999, -0.74697999, -0.74697999, ...,  0.30721301,
                   0.30721301,  0.30721301],
                 [ 1.46935877,  1.46935877,  1.46935877, ...,  0.3629416 ,
                   0.3629416 ,  0.13814133],
                 ...,
                 [ 0.89145609,  0.89145609,  0.89145609, ...,  0.3007356 ,
                   0.3007356 ,  0.3007356 ],
                 [ 0.13342492,  0.13342492,  0.17922369, ..., -0.26854499,
                  -0.16240555, -0.0922921 ],
                 [ 0.85255194,  0.85255194,  0.85255194, ...,  1.53291263,
                   1.53291263,  1.53291263]])
      • created_at :
        2020-06-10T18:21:37.261042
        arviz_version :
        0.8.3
        inference_library :
        emcee
        inference_library_version :
        3.0.2

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 40
        • draw: 1500
        • chain
          (chain)
          int64
          0 1 2 3 4 5 6 ... 34 35 36 37 38 39
          array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
                 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
                 36, 37, 38, 39])
        • draw
          (draw)
          int64
          0 1 2 3 4 ... 1496 1497 1498 1499
          array([   0,    1,    2, ..., 1497, 1498, 1499])
        • lp
          (chain, draw)
          float64
          -19.02 -17.53 ... -20.27 -20.27
          array([[-19.02258213, -17.53015266, -17.53015266, ..., -17.8496425 ,
                  -17.85983734, -17.85983734],
                 [-16.98092975, -16.98092975, -16.98092975, ..., -13.90696007,
                  -13.90696007, -13.90696007],
                 [-30.28871074, -30.28871074, -30.28871074, ..., -16.74925819,
                  -16.74925819, -12.9996326 ],
                 ...,
                 [-20.61328767, -20.61328767, -20.61328767, ..., -13.59218928,
                  -13.59218928, -13.59218928],
                 [-30.54403298, -30.54403298, -28.61897737, ..., -13.2645001 ,
                  -12.51696217, -17.11064559],
                 [-22.49391806, -22.49391806, -22.49391806, ..., -20.2684405 ,
                  -20.2684405 , -20.2684405 ]])
      • created_at :
        2020-06-10T18:21:37.254838
        arviz_version :
        0.8.3
        inference_library :
        emcee
        inference_library_version :
        3.0.2

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • arg_0_dim_0: 1
        • arg_1_dim_0: 8
        • arg_2_dim_0: 8
        • arg_0_dim_0
          (arg_0_dim_0)
          int64
          0
          array([0])
        • arg_1_dim_0
          (arg_1_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • arg_2_dim_0
          (arg_2_dim_0)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • arg_0
          (arg_0_dim_0)
          int64
          8
          array([8])
        • arg_1
          (arg_1_dim_0)
          float64
          28.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
          array([28.,  8., -3.,  7., -1.,  1., 18., 12.])
        • arg_2
          (arg_2_dim_0)
          float64
          15.0 10.0 16.0 ... 11.0 10.0 18.0
          array([15., 10., 16., 11.,  9., 11., 10., 18.])
      • created_at :
        2020-06-10T18:21:37.256560
        arviz_version :
        0.8.3
        inference_library :
        emcee
        inference_library_version :
        3.0.2

From CmdStanPy

[11]:
from cmdstanpy import CmdStanModel

schools_code = """
data {
    int<lower=0> J;
    real y[J];
    real<lower=0> sigma[J];
}

parameters {
    real mu;
    real<lower=0> tau;
    real theta_tilde[J];
}

transformed parameters {
    real theta[J];
    for (j in 1:J)
        theta[j] = mu + tau * theta_tilde[j];
}

model {
    mu ~ normal(0, 5);
    tau ~ cauchy(0, 5);
    theta_tilde ~ normal(0, 1);
    y ~ normal(theta, sigma);
}

generated quantities {
    vector[J] log_lik;
    vector[J] y_hat;
    for (j in 1:J) {
        log_lik[j] = normal_lpdf(y[j] | theta[j], sigma[j]);
        y_hat[j] = normal_rng(theta[j], sigma[j]);
    }
}
"""

with open("./eight_school.stan", "w") as f:
    print(schools_code, file=f)

stan_file = "./eight_school.stan"
stan_model = CmdStanModel(stan_file=stan_file)
stan_model.compile()

eight_school_data = {
    "J": 8,
    "y": np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
    "sigma": np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}

stan_fit = stan_model.sample(data=eight_school_data)

cmdstanpy_data = az.from_cmdstanpy(
    posterior=stan_fit,
    posterior_predictive="y_hat",
    observed_data={"y": eight_school_data["y"]},
    log_likelihood="log_lik",
    coords={"school": np.arange(eight_school_data["J"])},
    dims={
        "theta": ["school"],
        "y": ["school"],
        "log_lik": ["school"],
        "y_hat": ["school"],
        "theta_tilde": ["school"],
    },
)
cmdstanpy_data
INFO:cmdstanpy:compiling c++
INFO:cmdstanpy:compiled model file: /Users/percy/PycharmProjects/arviz/doc/notebooks/eight_school
INFO:cmdstanpy:found newer exe file, not recompiling
INFO:cmdstanpy:compiled model file: /Users/percy/PycharmProjects/arviz/doc/notebooks/eight_school
INFO:cmdstanpy:start chain 1
INFO:cmdstanpy:start chain 2
INFO:cmdstanpy:finish chain 2
INFO:cmdstanpy:start chain 3
INFO:cmdstanpy:finish chain 1
INFO:cmdstanpy:start chain 4
INFO:cmdstanpy:finish chain 3
INFO:cmdstanpy:finish chain 4
[11]:
arviz.InferenceData
    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 4
        • draw: 1000
        • school: 8
        • chain
          (chain)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • mu
          (chain, draw)
          float64
          2.908 8.134 3.037 ... 2.672 10.06
          array([[ 2.90813,  8.1337 ,  3.03685, ...,  3.49247,  2.69144,  2.77848],
                 [ 1.20098,  3.74153,  5.71236, ...,  5.38302,  1.55543,  6.85928],
                 [ 4.5479 ,  4.21596,  6.53758, ...,  1.8295 ,  6.26736, -2.83281],
                 [ 7.2998 ,  7.03214,  1.5383 , ...,  3.01368,  2.67249, 10.056  ]])
        • tau
          (chain, draw)
          float64
          3.566 1.06 1.014 ... 0.5414 5.807
          array([[ 3.56579  ,  1.06035  ,  1.0145   , ...,  0.295652 ,  0.152276 ,
                   1.27931  ],
                 [ 3.75274  ,  1.13823  ,  1.8422   , ...,  8.23264  ,  3.29958  ,
                   9.06202  ],
                 [ 0.0756374, 14.1684   ,  2.65082  , ...,  1.91313  ,  7.97043  ,
                   4.03989  ],
                 [ 0.0525536,  0.213029 ,  2.08631  , ...,  0.51228  ,  0.541425 ,
                   5.80725  ]])
        • theta_tilde
          (chain, draw, school)
          float64
          1.911 0.3988 ... 1.757 0.5014
          array([[[ 1.91055  ,  0.398843 , -0.206331 , ..., -1.11405  ,
                    1.85739  , -1.37968  ],
                  [-1.1159   , -0.447728 , -0.505903 , ...,  0.962855 ,
                   -0.601752 ,  0.89427  ],
                  [ 1.60719  , -0.596497 ,  0.151931 , ..., -1.28024  ,
                    0.930506 , -0.765005 ],
                  ...,
                  [-0.65252  , -0.933794 ,  1.11489  , ..., -0.606474 ,
                    0.323287 , -2.09671  ],
                  [-0.678068 , -0.391203 ,  0.887894 , ..., -0.721647 ,
                    0.131326 , -2.29018  ],
                  [ 0.0366895, -0.557451 ,  0.756044 , ...,  0.99686  ,
                    0.903742 , -0.308114 ]],
          
                 [[ 1.52082  ,  2.08589  , -1.2005   , ..., -0.602199 ,
                    1.88407  ,  0.109757 ],
                  [ 0.0451789, -1.61133  ,  1.96004  , ..., -0.548927 ,
                    0.375405 , -0.0377435],
                  [-0.216968 ,  1.40354  , -2.17544  , ...,  0.335058 ,
                   -0.201998 , -0.0420111],
                  ...,
                  [-1.24541  ,  1.44617  ,  1.26991  , ..., -0.517744 ,
                    1.06641  , -0.328943 ],
                  [-0.26795  , -0.471647 ,  0.916106 , ..., -0.0443553,
                    1.10523  ,  0.802313 ],
                  [ 0.860489 , -0.755706 , -0.221758 , ..., -0.881374 ,
                    1.02386  ,  2.26025  ]],
          
                 [[-0.728935 , -1.30284  , -0.725011 , ..., -1.13638  ,
                   -0.623346 ,  1.20411  ],
                  [ 0.877633 ,  1.57903  ,  0.657069 , ...,  1.18061  ,
                    0.873288 , -0.777553 ],
                  [ 1.92013  ,  1.41113  ,  0.565262 , ...,  0.892794 ,
                    1.17681  , -1.14554  ],
                  ...,
                  [-0.787386 , -1.34728  ,  0.938111 , ...,  0.212187 ,
                    1.5131   , -0.159953 ],
                  [ 1.29339  ,  0.0357047, -0.315845 , ...,  0.0184302,
                    0.789759 ,  0.502829 ],
                  [ 1.57545  ,  0.430001 ,  0.0687333, ...,  0.335712 ,
                    1.7016   , -1.64133  ]],
          
                 [[ 0.409093 ,  0.464062 ,  0.978    , ..., -0.780695 ,
                   -0.585484 ,  1.81793  ],
                  [ 0.076946 , -0.649097 , -0.768641 , ..., -0.375243 ,
                    0.651451 , -2.41116  ],
                  [-0.474311 , -0.847334 ,  0.663324 , ...,  0.276397 ,
                   -0.65441  ,  2.32434  ],
                  ...,
                  [-1.25161  ,  0.453957 ,  2.11518  , ..., -0.90933  ,
                    2.48317  , -0.782639 ],
                  [-0.137756 , -0.0470846, -1.45337  , ..., -2.4094   ,
                   -1.58137  ,  0.137089 ],
                  [ 1.41579  , -0.0828588,  1.27436  , ...,  0.247186 ,
                    1.75653  ,  0.501351 ]]])
        • theta
          (chain, draw, school)
          float64
          9.721 4.33 2.172 ... 20.26 12.97
          array([[[ 9.72074e+00,  4.33032e+00,  2.17239e+00, ..., -1.06433e+00,
                    9.53118e+00, -2.01152e+00],
                  [ 6.95047e+00,  7.65896e+00,  7.59727e+00, ...,  9.15466e+00,
                    7.49564e+00,  9.08194e+00],
                  [ 4.66734e+00,  2.43171e+00,  3.19099e+00, ...,  1.73805e+00,
                    3.98085e+00,  2.26076e+00],
                  ...,
                  [ 3.29955e+00,  3.21639e+00,  3.82208e+00, ...,  3.31316e+00,
                    3.58805e+00,  2.87257e+00],
                  [ 2.58818e+00,  2.63187e+00,  2.82664e+00, ...,  2.58155e+00,
                    2.71143e+00,  2.34270e+00],
                  [ 2.82542e+00,  2.06533e+00,  3.74569e+00, ...,  4.05377e+00,
                    3.93464e+00,  2.38430e+00]],
          
                 [[ 6.90821e+00,  9.02878e+00, -3.30420e+00, ..., -1.05892e+00,
                    8.27142e+00,  1.61287e+00],
                  [ 3.79295e+00,  1.90747e+00,  5.97250e+00, ...,  3.11672e+00,
                    4.16882e+00,  3.69857e+00],
                  [ 5.31266e+00,  8.29796e+00,  1.70476e+00, ...,  6.32960e+00,
                    5.34024e+00,  5.63497e+00],
                  ...,
                  [-4.86998e+00,  1.72888e+01,  1.58377e+01, ...,  1.12062e+00,
                    1.41624e+01,  2.67495e+00],
                  [ 6.71302e-01, -8.13246e-04,  4.57819e+00, ...,  1.40907e+00,
                    5.20222e+00,  4.20272e+00],
                  [ 1.46570e+01,  1.10534e-02,  4.84970e+00, ..., -1.12774e+00,
                    1.61376e+01,  2.73417e+01]],
          
                 [[ 4.49277e+00,  4.44936e+00,  4.49306e+00, ...,  4.46195e+00,
                    4.50075e+00,  4.63898e+00],
                  [ 1.66506e+01,  2.65883e+01,  1.35256e+01, ...,  2.09433e+01,
                    1.65890e+01, -6.80072e+00],
                  [ 1.16275e+01,  1.02782e+01,  8.03598e+00, ...,  8.90421e+00,
                    9.65709e+00,  3.50097e+00],
                  ...,
                  [ 3.23128e-01, -7.48028e-01,  3.62423e+00, ...,  2.23544e+00,
                    4.72425e+00,  1.52349e+00],
                  [ 1.65762e+01,  6.55194e+00,  3.74994e+00, ...,  6.41426e+00,
                    1.25621e+01,  1.02751e+01],
                  [ 3.53185e+00, -1.09566e+00, -2.55514e+00, ..., -1.47657e+00,
                    4.04147e+00, -9.46361e+00]],
          
                 [[ 7.32130e+00,  7.32419e+00,  7.35120e+00, ...,  7.25878e+00,
                    7.26903e+00,  7.39534e+00],
                  [ 7.04853e+00,  6.89386e+00,  6.86839e+00, ...,  6.95220e+00,
                    7.17091e+00,  6.51849e+00],
                  [ 5.48734e-01, -2.29508e-01,  2.92220e+00, ...,  2.11494e+00,
                    1.72992e-01,  6.38759e+00],
                  ...,
                  [ 2.37250e+00,  3.24623e+00,  4.09725e+00, ...,  2.54785e+00,
                    4.28576e+00,  2.61275e+00],
                  [ 2.59791e+00,  2.64700e+00,  1.88560e+00, ...,  1.36798e+00,
                    1.81630e+00,  2.74672e+00],
                  [ 1.82778e+01,  9.57482e+00,  1.74565e+01, ...,  1.14915e+01,
                    2.02566e+01,  1.29675e+01]]])
      • created_at :
        2020-06-10T18:21:56.176067
        arviz_version :
        0.8.3
        inference_library :
        cmdstanpy
        inference_library_version :
        0.8.0

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 4
        • draw: 1000
        • school: 8
        • chain
          (chain)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • y_hat
          (chain, draw, school)
          float64
          27.32 16.59 19.23 ... 15.28 -14.33
          array([[[ 27.316   ,  16.5918  ,  19.2331  , ...,  -2.68653 ,
                    12.2412  ,  27.0189  ],
                  [ 13.7773  ,  -4.34203 ,   3.61368 , ...,   2.72659 ,
                    13.737   ,   2.31227 ],
                  [ -3.79392 ,  -0.568726, -16.99    , ...,   8.77864 ,
                     6.83554 , -24.1435  ],
                  ...,
                  [ 16.0011  ,  16.3268  ,   0.235298, ..., -14.9994  ,
                     6.60276 ,  -0.33642 ],
                  [ -3.59346 ,  -7.50548 ,  -0.90007 , ...,  -0.173541,
                     3.61428 ,  25.8661  ],
                  [  5.06708 ,  -4.07957 , -23.1559  , ...,   7.18739 ,
                     9.59156 ,   5.01793 ]],
          
                 [[ -0.843751,  -4.98264 , -18.7942  , ...,  -6.34356 ,
                   -11.4954  , -30.0613  ],
                  [-32.9141  ,  -6.91807 ,  -6.90439 , ...,  10.1167  ,
                     3.70618 ,   8.15487 ],
                  [  2.88749 ,   0.686142,  24.0905  , ...,   9.77811 ,
                    31.1765  , -18.8176  ],
                  ...,
                  [-10.4054  ,  38.8779  ,  -1.72784 , ...,   2.10858 ,
                     1.71828 , -41.049   ],
                  [-34.6393  ,  -8.05134 ,   0.299065, ...,  -5.08346 ,
                    14.0737  ,  18.2229  ],
                  [ 20.5415  ,  -7.11264 ,  16.6271  , ...,  -6.10246 ,
                    16.3215  ,  28.9235  ]],
          
                 [[ -0.601871, -11.7324  ,  20.1891  , ...,  14.0161  ,
                    -1.10264 ,  -0.811892],
                  [ 16.1775  ,  19.1952  ,   7.63344 , ...,  15.3313  ,
                    20.5808  ,  -0.475661],
                  [ -6.71155 ,  -3.46014 ,  15.4774  , ...,  22.6551  ,
                    -6.43601 ,  23.9684  ],
                  ...,
                  [ 19.7332  , -20.677   ,  24.276   , ...,  12.3559  ,
                    11.5496  ,  17.943   ],
                  [ 13.6132  ,   5.89891 ,  -6.70882 , ...,   5.5949  ,
                    16.5097  , -13.9093  ],
                  [ 26.0067  ,  -2.92887 ,  28.0343  , ..., -11.2195  ,
                     3.37155 ,  -8.39441 ]],
          
                 [[ -1.77315 ,  -0.850641,  31.9772  , ...,  12.9403  ,
                    19.1804  , -11.9612  ],
                  [ 12.9344  ,  -7.44461 ,   0.504742, ..., -11.9935  ,
                    -5.35724 ,  20.562   ],
                  [-11.582   ,  -9.02636 ,  18.8871  , ...,   2.61293 ,
                   -10.874   ,  33.0402  ],
                  ...,
                  [ 15.5324  ,  14.9454  ,   7.0026  , ...,  -0.143009,
                     3.01618 ,  -5.04935 ],
                  [-14.324   ,  -4.90844 , -12.5231  , ..., -15.5133  ,
                     7.05567 , -27.792   ],
                  [ 15.8131  ,  14.6397  ,  33.993   , ...,   1.04319 ,
                    15.2797  , -14.3346  ]]])
      • created_at :
        2020-06-10T18:21:56.187926
        arviz_version :
        0.8.3
        inference_library :
        cmdstanpy
        inference_library_version :
        0.8.0

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 4
        • draw: 1000
        • school: 8
        • chain
          (chain)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • log_lik
          (chain, draw, school)
          float64
          -4.37 -3.289 ... -3.247 -3.811
          array([[[-4.3695 , -3.28886, -3.74378, ..., -3.33444, -3.58013,
                   -4.11228],
                  [-4.61162, -3.22211, -3.91087, ..., -3.59162, -3.77323,
                   -3.82245],
                  [-4.8368 , -3.37655, -3.76639, ..., -3.31908, -4.20421,
                   -3.95569],
                  ...,
                  [-4.98279, -3.33594, -3.78243, ..., -3.33894, -4.26005,
                   -3.93788],
                  [-5.06201, -3.36561, -3.75784, ..., -3.32717, -4.39022,
                   -3.95324],
                  [-5.03534, -3.39763, -3.7804 , ..., -3.35537, -4.21069,
                   -3.952  ]],
          
                 [[-4.61557, -3.22682, -3.69171, ..., -3.33435, -3.69475,
                   -3.97581],
                  [-4.92917, -3.40712, -3.84876, ..., -3.33535, -4.17803,
                   -3.91566],
                  [-4.7708 , -3.22197, -3.73476, ..., -3.43421, -4.02287,
                   -3.87183],
                  ...,
                  [-6.02796, -3.65293, -4.38461, ..., -3.31689, -3.29516,
                   -3.9435 ],
                  [-5.28667, -3.54159, -3.80369, ..., -3.31753, -4.04044,
                   -3.90313],
                  [-4.02262, -3.54064, -3.81187, ..., -3.33554, -3.23887,
                   -4.17253]],
          
                 [[-4.85497, -3.28456, -3.80119, ..., -3.36636, -4.13267,
                   -3.89293],
                  [-3.91323, -4.94915, -4.22492, ..., -4.96036, -3.23148,
                   -4.35478],
                  [-4.22267, -3.24747, -3.9294 , ..., -3.575  , -3.56954,
                   -3.92078],
                  ...,
                  [-5.32923, -3.60416, -3.77723, ..., -3.32314, -4.10275,
                   -3.97869],
                  [-3.91699, -3.23201, -3.78051, ..., -3.43797, -3.36938,
                   -3.8139 ],
                  [-4.95741, -3.63518, -3.69191, ..., -3.34218, -4.19573,
                   -4.52025]],
          
                 [[-4.57723, -3.22381, -3.9008 , ..., -3.4787 , -3.79729,
                   -3.84203],
                  [-4.60246, -3.22764, -3.88173, ..., -3.46323, -3.80787,
                   -3.85568],
                  [-5.30159, -3.56015, -3.76003, ..., -3.32197, -4.81053,
                   -3.85792],
                  ...,
                  [-5.08647, -3.33452, -3.78991, ..., -3.32673, -4.16193,
                   -3.9453 ],
                  [-5.06091, -3.3648 , -3.73815, ..., -3.31739, -4.53108,
                   -3.94144],
                  [-3.83703, -3.23392, -4.50885, ..., -3.77167, -3.24699,
                   -3.81075]]])
      • created_at :
        2020-06-10T18:21:56.190772
        arviz_version :
        0.8.3
        inference_library :
        cmdstanpy
        inference_library_version :
        0.8.0

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 4
        • draw: 1000
        • chain
          (chain)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • lp
          (chain, draw)
          float64
          -7.117 -8.525 ... -11.38 -11.14
          array([[ -7.11711,  -8.52527,  -8.34257, ...,  -8.99953, -10.3924 ,
                   -5.12677],
                 [ -7.40979,  -8.6973 ,  -8.36134, ...,  -9.30419,  -4.65713,
                   -9.11054],
                 [ -9.35431,  -9.76551,  -7.86183, ...,  -7.19184,  -5.21445,
                   -7.71352],
                 [-10.2665 , -13.9631 ,  -9.83918, ..., -13.5776 , -11.3765 ,
                  -11.145  ]])
        • accept_stat
          (chain, draw)
          float64
          0.9616 0.9694 ... 0.9886 0.429
          array([[0.96156 , 0.969437, 0.984633, ..., 0.966525, 0.988819, 0.919061],
                 [0.892384, 0.952504, 0.999717, ..., 0.981023, 0.945826, 0.627332],
                 [1.      , 0.997771, 0.14691 , ..., 1.      , 1.      , 0.459213],
                 [0.714025, 0.911832, 1.      , ..., 0.823447, 0.988555, 0.428968]])
        • stepsize
          (chain, draw)
          float64
          0.4064 0.4064 ... 0.4323 0.4323
          array([[0.406405, 0.406405, 0.406405, ..., 0.406405, 0.406405, 0.406405],
                 [0.466926, 0.466926, 0.466926, ..., 0.466926, 0.466926, 0.466926],
                 [0.50536 , 0.50536 , 0.50536 , ..., 0.50536 , 0.50536 , 0.50536 ],
                 [0.432263, 0.432263, 0.432263, ..., 0.432263, 0.432263, 0.432263]])
        • treedepth
          (chain, draw)
          int64
          3 4 3 3 4 3 4 3 ... 3 3 3 3 3 3 3 3
          array([[3, 4, 3, ..., 3, 3, 3],
                 [3, 3, 3, ..., 3, 3, 3],
                 [3, 3, 3, ..., 3, 3, 3],
                 [3, 3, 3, ..., 3, 3, 3]])
        • n_leapfrog
          (chain, draw)
          int64
          7 15 7 7 15 7 15 ... 7 7 15 7 15 7
          array([[ 7, 15,  7, ...,  7,  7,  7],
                 [ 7,  7,  7, ...,  7,  7,  7],
                 [ 7,  7,  7, ...,  7,  7,  7],
                 [15, 15,  7, ...,  7, 15,  7]])
        • diverging
          (chain, draw)
          bool
          False False False ... False False
          array([[False, False, False, ..., False, False, False],
                 [False, False, False, ..., False, False, False],
                 [False, False, False, ..., False, False, False],
                 [False, False, False, ..., False, False, False]])
        • energy
          (chain, draw)
          float64
          13.56 12.9 13.65 ... 20.86 22.16
          array([[13.556  , 12.8971 , 13.6523 , ..., 11.4512 , 14.1995 , 12.5183 ],
                 [12.3025 , 16.388  , 10.6192 , ..., 19.1564 , 12.9302 , 13.1066 ],
                 [14.6137 , 11.6894 , 14.2455 , ...,  9.98162,  9.17208, 15.7546 ],
                 [19.118  , 19.03   , 16.7125 , ..., 18.6839 , 20.8571 , 22.1571 ]])
      • created_at :
        2020-06-10T18:21:56.182646
        arviz_version :
        0.8.3
        inference_library :
        cmdstanpy
        inference_library_version :
        0.8.0

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • school: 8
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • y
          (school)
          float64
          28.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
          array([28.,  8., -3.,  7., -1.,  1., 18., 12.])
      • created_at :
        2020-06-10T18:21:56.189062
        arviz_version :
        0.8.3
        inference_library :
        cmdstanpy
        inference_library_version :
        0.8.0

From CmdStan

See from_cmdstan for details.

CmdStan helpers

[12]:
# save for CmdStan example (needs CmdStanPy run)
stan_fit.save_csvfiles(dir="sample_data")
[13]:
schools_code = """
data {
    int<lower=0> J;
    real y[J];
    real<lower=0> sigma[J];
}

parameters {
    real mu;
    real<lower=0> tau;
    real theta_tilde[J];
}

transformed parameters {
    real theta[J];
    for (j in 1:J)
        theta[j] = mu + tau * theta_tilde[j];
}

model {
    mu ~ normal(0, 5);
    tau ~ cauchy(0, 5);
    theta_tilde ~ normal(0, 1);
    y ~ normal(theta, sigma);
}

generated quantities {
    vector[J] log_lik;
    vector[J] y_hat;
    for (j in 1:J) {
        log_lik[j] = normal_lpdf(y[j] | theta[j], sigma[j]);
        y_hat[j] = normal_rng(theta[j], sigma[j]);
    }
}
"""

with open("./eight_school.stan", "w") as f:
    print(schools_code, file=f)
[14]:
eight_school_data = {
    "J": 8,
    "y": np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
    "sigma": np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}
[15]:
import pystan

pystan.stan_rdump(eight_school_data, "./eight_school.data.R")
[16]:
# Bash shell
#
# $ cd cmdstan
# $ make build
# $ make path/to/eight_school
# $ cd path/to
# $ for i in {1..4}
#   do
#     ./eight_school sample random seed=12345 \
#       id=$i data file=eight_school.data.R \
#       output file=sample_data/eight_school_samples-$i.csv &
#   done
# $
[17]:
# Let's use .stan and .csv files created/saved by the CmdStanPy procedure

# glob string
posterior_glob = "sample_data/eight_school-*-[0-9].csv"
# list of paths
# posterior_list =  [
#     "sample_data/eight_school-*-1.csv",
#     "sample_data/eight_school-*-2.csv",
#     "sample_data/eight_school-*-3.csv",
#     "sample_data/eight_school-*-4.csv",
# ]

obs_data_path = "./eight_school.data.R"

cmdstan_data = az.from_cmdstan(
    posterior=posterior_glob,
    posterior_predictive="y_hat",
    observed_data=obs_data_path,
    observed_data_var="y",
    log_likelihood="log_lik",
    coords={"school": np.arange(eight_school_data["J"])},
    dims={
        "theta": ["school"],
        "y": ["school"],
        "log_lik": ["school"],
        "y_hat": ["school"],
        "theta_tilde": ["school"],
    },
)
cmdstan_data
arviz.data.io_cmdstan - INFO - glob found 12 files for 'posterior':
1: sample_data/eight_school-202006100113-1.csv
2: sample_data/eight_school-202006100113-2.csv
3: sample_data/eight_school-202006100113-3.csv
4: sample_data/eight_school-202006100113-4.csv
5: sample_data/eight_school-202006102306-1.csv
6: sample_data/eight_school-202006102306-2.csv
7: sample_data/eight_school-202006102306-3.csv
8: sample_data/eight_school-202006102306-4.csv
9: sample_data/eight_school-202006102351-1.csv
10: sample_data/eight_school-202006102351-2.csv
11: sample_data/eight_school-202006102351-3.csv
12: sample_data/eight_school-202006102351-4.csv
INFO:arviz.data.io_cmdstan:glob found 12 files for 'posterior':
1: sample_data/eight_school-202006100113-1.csv
2: sample_data/eight_school-202006100113-2.csv
3: sample_data/eight_school-202006100113-3.csv
4: sample_data/eight_school-202006100113-4.csv
5: sample_data/eight_school-202006102306-1.csv
6: sample_data/eight_school-202006102306-2.csv
7: sample_data/eight_school-202006102306-3.csv
8: sample_data/eight_school-202006102306-4.csv
9: sample_data/eight_school-202006102351-1.csv
10: sample_data/eight_school-202006102351-2.csv
11: sample_data/eight_school-202006102351-3.csv
12: sample_data/eight_school-202006102351-4.csv
[17]:
arviz.InferenceData
    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 12
        • draw: 1000
        • school: 8
        • chain
          (chain)
          int64
          0 1 2 3 4 5 6 7 8 9 10 11
          array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • mu
          (chain, draw)
          float64
          3.692 16.11 2.111 ... 2.672 10.06
          array([[ 3.69234  , 16.1054   ,  2.11087  , ...,  8.19067  ,  2.92031  ,
                   1.03508  ],
                 [-1.71907  , 10.6737   ,  5.45426  , ..., 11.9617   , -0.0648748,
                   2.95623  ],
                 [ 6.44788  ,  5.00457  ,  9.41369  , ..., -0.588549 ,  3.43133  ,
                   4.04414  ],
                 ...,
                 [ 1.20098  ,  3.74153  ,  5.71236  , ...,  5.38302  ,  1.55543  ,
                   6.85928  ],
                 [ 4.5479   ,  4.21596  ,  6.53758  , ...,  1.8295   ,  6.26736  ,
                  -2.83281  ],
                 [ 7.2998   ,  7.03214  ,  1.5383   , ...,  3.01368  ,  2.67249  ,
                  10.056    ]])
        • tau
          (chain, draw)
          float64
          6.108 3.582 4.862 ... 0.5414 5.807
          array([[ 6.1083   ,  3.58214  ,  4.86183  , ...,  4.47256  ,  1.48153  ,
                  12.0573   ],
                 [ 6.89254  ,  2.58141  ,  0.803485 , ...,  2.4602   ,  0.599099 ,
                   0.97436  ],
                 [ 7.54792  ,  3.12201  ,  0.912562 , ...,  1.33408  ,  5.39912  ,
                   1.91634  ],
                 ...,
                 [ 3.75274  ,  1.13823  ,  1.8422   , ...,  8.23264  ,  3.29958  ,
                   9.06202  ],
                 [ 0.0756374, 14.1684   ,  2.65082  , ...,  1.91313  ,  7.97043  ,
                   4.03989  ],
                 [ 0.0525536,  0.213029 ,  2.08631  , ...,  0.51228  ,  0.541425 ,
                   5.80725  ]])
        • theta_tilde
          (chain, draw, school)
          float64
          0.1507 -0.07589 ... 1.757 0.5014
          array([[[ 0.150693  , -0.0758865 ,  0.222117  , ..., -2.20267   ,
                    0.438651  ,  0.0774884 ],
                  [-0.690449  , -0.61755   , -0.285046  , ...,  0.905517  ,
                   -0.121017  , -0.0131619 ],
                  [-0.89236   ,  0.30326   , -0.0355057 , ..., -1.07422   ,
                   -0.238142  ,  0.145528  ],
                  ...,
                  [ 1.87184   , -1.41064   ,  0.60382   , ..., -0.52979   ,
                   -0.753925  ,  1.01887   ],
                  [ 0.00838069, -0.665387  , -0.0369778 , ..., -0.283951  ,
                    0.982918  ,  0.749047  ],
                  [ 1.60212   ,  1.30792   ,  0.0776785 , ...,  0.312027  ,
                    0.669589  ,  0.215141  ]],
          
                 [[ 1.8168    , -0.0393204 ,  0.134036  , ...,  0.511469  ,
                    0.916789  ,  0.526759  ],
                  [-1.9468    , -0.116474  , -0.809836  , ..., -0.355235  ,
                    0.339156  , -0.180418  ],
                  [ 1.29277   , -0.441339  , -2.04181   , ..., -0.40026   ,
                    0.39932   ,  0.263459  ],
                  ...,
                  [ 0.131124  ,  0.901146  , -0.759669  , ..., -0.87047   ,
                   -0.700857  , -0.868739  ],
                  [-0.815558  , -1.32762   ,  0.935707  , ...,  0.348515  ,
                   -0.542335  ,  0.49039   ],
                  [-1.59891   , -1.05952   , -0.0429794 , ...,  0.353703  ,
                    0.096935  , -0.824714  ]],
          
                 [[ 0.919008  ,  0.427259  , -1.39858   , ..., -0.803076  ,
                    1.4394    , -1.0618    ],
                  [-0.666333  ,  0.134364  , -1.69212   , ..., -1.66072   ,
                    0.569682  , -1.16606   ],
                  [-0.558085  , -0.793793  ,  0.566323  , ..., -0.395261  ,
                    0.948139  , -0.380621  ],
                  ...,
                  [ 0.666746  ,  0.252036  ,  0.0992795 , ..., -1.08194   ,
                   -1.23669   ,  1.74524   ],
                  [ 0.91375   ,  0.651899  ,  0.0450728 , ...,  0.794356  ,
                    2.65045   , -0.710101  ],
                  [ 0.231504  ,  0.297168  ,  0.0153996 , ...,  1.25694   ,
                    2.37274   , -0.873043  ]],
          
                 ...,
          
                 [[ 1.52082   ,  2.08589   , -1.2005    , ..., -0.602199  ,
                    1.88407   ,  0.109757  ],
                  [ 0.0451789 , -1.61133   ,  1.96004   , ..., -0.548927  ,
                    0.375405  , -0.0377435 ],
                  [-0.216968  ,  1.40354   , -2.17544   , ...,  0.335058  ,
                   -0.201998  , -0.0420111 ],
                  ...,
                  [-1.24541   ,  1.44617   ,  1.26991   , ..., -0.517744  ,
                    1.06641   , -0.328943  ],
                  [-0.26795   , -0.471647  ,  0.916106  , ..., -0.0443553 ,
                    1.10523   ,  0.802313  ],
                  [ 0.860489  , -0.755706  , -0.221758  , ..., -0.881374  ,
                    1.02386   ,  2.26025   ]],
          
                 [[-0.728935  , -1.30284   , -0.725011  , ..., -1.13638   ,
                   -0.623346  ,  1.20411   ],
                  [ 0.877633  ,  1.57903   ,  0.657069  , ...,  1.18061   ,
                    0.873288  , -0.777553  ],
                  [ 1.92013   ,  1.41113   ,  0.565262  , ...,  0.892794  ,
                    1.17681   , -1.14554   ],
                  ...,
                  [-0.787386  , -1.34728   ,  0.938111  , ...,  0.212187  ,
                    1.5131    , -0.159953  ],
                  [ 1.29339   ,  0.0357047 , -0.315845  , ...,  0.0184302 ,
                    0.789759  ,  0.502829  ],
                  [ 1.57545   ,  0.430001  ,  0.0687333 , ...,  0.335712  ,
                    1.7016    , -1.64133   ]],
          
                 [[ 0.409093  ,  0.464062  ,  0.978     , ..., -0.780695  ,
                   -0.585484  ,  1.81793   ],
                  [ 0.076946  , -0.649097  , -0.768641  , ..., -0.375243  ,
                    0.651451  , -2.41116   ],
                  [-0.474311  , -0.847334  ,  0.663324  , ...,  0.276397  ,
                   -0.65441   ,  2.32434   ],
                  ...,
                  [-1.25161   ,  0.453957  ,  2.11518   , ..., -0.90933   ,
                    2.48317   , -0.782639  ],
                  [-0.137756  , -0.0470846 , -1.45337   , ..., -2.4094    ,
                   -1.58137   ,  0.137089  ],
                  [ 1.41579   , -0.0828588 ,  1.27436   , ...,  0.247186  ,
                    1.75653   ,  0.501351  ]]])
        • theta
          (chain, draw, school)
          float64
          4.613 3.229 5.049 ... 20.26 12.97
          array([[[ 4.61281e+00,  3.22880e+00,  5.04910e+00, ..., -9.76221e+00,
                    6.37175e+00,  4.16566e+00],
                  [ 1.36322e+01,  1.38933e+01,  1.50844e+01, ...,  1.93491e+01,
                    1.56719e+01,  1.60583e+01],
                  [-2.22763e+00,  3.58527e+00,  1.93825e+00, ..., -3.11180e+00,
                    9.53064e-01,  2.81840e+00],
                  ...,
                  [ 1.65626e+01,  1.88149e+00,  1.08913e+01, ...,  5.82115e+00,
                    4.81870e+00,  1.27476e+01],
                  [ 2.93273e+00,  1.93452e+00,  2.86553e+00, ...,  2.49963e+00,
                    4.37654e+00,  4.03005e+00],
                  [ 2.03524e+01,  1.68052e+01,  1.97168e+00, ...,  4.79731e+00,
                    9.10855e+00,  3.62912e+00]],
          
                 [[ 1.08033e+01, -1.99009e+00, -7.95223e-01, ...,  1.80625e+00,
                    4.59993e+00,  1.91163e+00],
                  [ 5.64823e+00,  1.03731e+01,  8.58322e+00, ...,  9.75673e+00,
                    1.15492e+01,  1.02080e+01],
                  [ 6.49298e+00,  5.09965e+00,  3.81370e+00, ...,  5.13266e+00,
                    5.77511e+00,  5.66595e+00],
                  ...,
                  [ 1.22843e+01,  1.41787e+01,  1.00928e+01, ...,  9.82016e+00,
                    1.02374e+01,  9.82442e+00],
                  [-5.53475e-01, -8.60252e-01,  4.95706e-01, ...,  1.43920e-01,
                   -3.89787e-01,  2.28918e-01],
                  [ 1.39832e+00,  1.92387e+00,  2.91435e+00, ...,  3.30086e+00,
                    3.05068e+00,  2.15266e+00]],
          
                 [[ 1.33845e+01,  9.67280e+00, -4.10847e+00, ...,  3.86324e-01,
                    1.73124e+01, -1.56653e+00],
                  [ 2.92428e+00,  5.42406e+00, -2.78235e-01, ..., -1.80204e-01,
                    6.78313e+00,  1.36413e+00],
                  [ 8.90440e+00,  8.68930e+00,  9.93049e+00, ...,  9.05299e+00,
                    1.02789e+01,  9.06635e+00],
                  ...,
                  [ 3.00946e-01, -2.52311e-01, -4.56102e-01, ..., -2.03194e+00,
                   -2.23840e+00,  1.73975e+00],
                  [ 8.36477e+00,  6.95101e+00,  3.67468e+00, ...,  7.72015e+00,
                    1.77414e+01, -4.02591e-01],
                  [ 4.48778e+00,  4.61362e+00,  4.07365e+00, ...,  6.45287e+00,
                    8.59112e+00,  2.37110e+00]],
          
                 ...,
          
                 [[ 6.90821e+00,  9.02878e+00, -3.30420e+00, ..., -1.05892e+00,
                    8.27142e+00,  1.61287e+00],
                  [ 3.79295e+00,  1.90747e+00,  5.97250e+00, ...,  3.11672e+00,
                    4.16882e+00,  3.69857e+00],
                  [ 5.31266e+00,  8.29796e+00,  1.70476e+00, ...,  6.32960e+00,
                    5.34024e+00,  5.63497e+00],
                  ...,
                  [-4.86998e+00,  1.72888e+01,  1.58377e+01, ...,  1.12062e+00,
                    1.41624e+01,  2.67495e+00],
                  [ 6.71302e-01, -8.13246e-04,  4.57819e+00, ...,  1.40907e+00,
                    5.20222e+00,  4.20272e+00],
                  [ 1.46570e+01,  1.10534e-02,  4.84970e+00, ..., -1.12774e+00,
                    1.61376e+01,  2.73417e+01]],
          
                 [[ 4.49277e+00,  4.44936e+00,  4.49306e+00, ...,  4.46195e+00,
                    4.50075e+00,  4.63898e+00],
                  [ 1.66506e+01,  2.65883e+01,  1.35256e+01, ...,  2.09433e+01,
                    1.65890e+01, -6.80072e+00],
                  [ 1.16275e+01,  1.02782e+01,  8.03598e+00, ...,  8.90421e+00,
                    9.65709e+00,  3.50097e+00],
                  ...,
                  [ 3.23128e-01, -7.48028e-01,  3.62423e+00, ...,  2.23544e+00,
                    4.72425e+00,  1.52349e+00],
                  [ 1.65762e+01,  6.55194e+00,  3.74994e+00, ...,  6.41426e+00,
                    1.25621e+01,  1.02751e+01],
                  [ 3.53185e+00, -1.09566e+00, -2.55514e+00, ..., -1.47657e+00,
                    4.04147e+00, -9.46361e+00]],
          
                 [[ 7.32130e+00,  7.32419e+00,  7.35120e+00, ...,  7.25878e+00,
                    7.26903e+00,  7.39534e+00],
                  [ 7.04853e+00,  6.89386e+00,  6.86839e+00, ...,  6.95220e+00,
                    7.17091e+00,  6.51849e+00],
                  [ 5.48734e-01, -2.29508e-01,  2.92220e+00, ...,  2.11494e+00,
                    1.72992e-01,  6.38759e+00],
                  ...,
                  [ 2.37250e+00,  3.24623e+00,  4.09725e+00, ...,  2.54785e+00,
                    4.28576e+00,  2.61275e+00],
                  [ 2.59791e+00,  2.64700e+00,  1.88560e+00, ...,  1.36798e+00,
                    1.81630e+00,  2.74672e+00],
                  [ 1.82778e+01,  9.57482e+00,  1.74565e+01, ...,  1.14915e+01,
                    2.02566e+01,  1.29675e+01]]])
      • created_at :
        2020-06-10T18:21:57.128552
        arviz_version :
        0.8.3

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 12
        • draw: 1000
        • school: 8
        • chain
          (chain)
          int64
          0 1 2 3 4 5 6 7 8 9 10 11
          array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • y_hat
          (chain, draw, school)
          float64
          -10.93 11.6 11.14 ... 15.28 -14.33
          array([[[-10.9346  ,  11.6037  ,  11.1382  , ...,  -4.97421 ,
                    -6.09248 ,  15.0512  ],
                  [ -3.69064 ,  14.6682  ,  22.4837  , ...,  23.5671  ,
                    14.8374  ,   9.00593 ],
                  [  0.408807,  -7.37329 ,  -1.04588 , ...,  -6.87661 ,
                     3.75974 , -11.8118  ],
                  ...,
                  [ 20.0649  ,   4.67947 ,  34.8539  , ...,  19.3071  ,
                    -1.81022 ,  10.6627  ],
                  [ 20.023   ,  -3.45228 , -16.6117  , ...,   4.34399 ,
                    19.4159  ,   4.02906 ],
                  [ 12.6708  ,   9.25176 ,  18.6282  , ...,  -0.56782 ,
                    -5.90848 , -24.1042  ]],
          
                 [[ 25.585   ,   2.60382 , -22.731   , ...,  12.1856  ,
                   -24.8332  ,  -7.97341 ],
                  [  3.05847 ,  19.6072  ,   9.67468 , ...,  -9.57937 ,
                    -5.97203 ,   3.83901 ],
                  [ -2.96353 ,   1.59361 ,  34.3077  , ..., -16.9225  ,
                     5.94989 ,  12.7261  ],
                  ...,
                  [-30.3258  ,  25.8939  ,  11.0092  , ...,  10.8265  ,
                     5.90875 , -27.5675  ],
                  [ 12.7005  ,  -4.70354 , -11.1986  , ...,  -7.05527 ,
                    -6.65953 ,  35.0723  ],
                  [ 10.4867  ,   5.49925 ,  -5.00058 , ...,  16.8872  ,
                    -1.90614 ,   5.35349 ]],
          
                 [[ 26.4483  ,   5.39621 , -18.0307  , ..., -16.5188  ,
                    13.9216  ,  -3.97292 ],
                  [ -7.85832 ,   4.44009 ,   5.35032 , ..., -10.6668  ,
                    20.5908  , -12.8477  ],
                  [ -1.72751 ,  15.6356  ,  -7.37621 , ...,  36.3976  ,
                     9.78589 ,   8.58118 ],
                  ...,
                  [ -2.08977 ,  13.1182  ,  -8.81588 , ...,  -9.16025 ,
                   -11.6879  , -28.6293  ],
                  [ -1.44321 ,   3.20826 ,  -4.6157  , ...,  23.3955  ,
                    18.8133  , -21.3375  ],
                  [ 10.1546  ,  16.7743  , -13.0238  , ...,  -5.73191 ,
                    12.5278  ,   9.80171 ]],
          
                 ...,
          
                 [[ -0.843751,  -4.98264 , -18.7942  , ...,  -6.34356 ,
                   -11.4954  , -30.0613  ],
                  [-32.9141  ,  -6.91807 ,  -6.90439 , ...,  10.1167  ,
                     3.70618 ,   8.15487 ],
                  [  2.88749 ,   0.686142,  24.0905  , ...,   9.77811 ,
                    31.1765  , -18.8176  ],
                  ...,
                  [-10.4054  ,  38.8779  ,  -1.72784 , ...,   2.10858 ,
                     1.71828 , -41.049   ],
                  [-34.6393  ,  -8.05134 ,   0.299065, ...,  -5.08346 ,
                    14.0737  ,  18.2229  ],
                  [ 20.5415  ,  -7.11264 ,  16.6271  , ...,  -6.10246 ,
                    16.3215  ,  28.9235  ]],
          
                 [[ -0.601871, -11.7324  ,  20.1891  , ...,  14.0161  ,
                    -1.10264 ,  -0.811892],
                  [ 16.1775  ,  19.1952  ,   7.63344 , ...,  15.3313  ,
                    20.5808  ,  -0.475661],
                  [ -6.71155 ,  -3.46014 ,  15.4774  , ...,  22.6551  ,
                    -6.43601 ,  23.9684  ],
                  ...,
                  [ 19.7332  , -20.677   ,  24.276   , ...,  12.3559  ,
                    11.5496  ,  17.943   ],
                  [ 13.6132  ,   5.89891 ,  -6.70882 , ...,   5.5949  ,
                    16.5097  , -13.9093  ],
                  [ 26.0067  ,  -2.92887 ,  28.0343  , ..., -11.2195  ,
                     3.37155 ,  -8.39441 ]],
          
                 [[ -1.77315 ,  -0.850641,  31.9772  , ...,  12.9403  ,
                    19.1804  , -11.9612  ],
                  [ 12.9344  ,  -7.44461 ,   0.504742, ..., -11.9935  ,
                    -5.35724 ,  20.562   ],
                  [-11.582   ,  -9.02636 ,  18.8871  , ...,   2.61293 ,
                   -10.874   ,  33.0402  ],
                  ...,
                  [ 15.5324  ,  14.9454  ,   7.0026  , ...,  -0.143009,
                     3.01618 ,  -5.04935 ],
                  [-14.324   ,  -4.90844 , -12.5231  , ..., -15.5133  ,
                     7.05567 , -27.792   ],
                  [ 15.8131  ,  14.6397  ,  33.993   , ...,   1.04319 ,
                    15.2797  , -14.3346  ]]])
      • created_at :
        2020-06-10T18:21:57.962326
        arviz_version :
        0.8.3

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 12
        • draw: 1000
        • school: 8
        • chain
          (chain)
          int64
          0 1 2 3 4 5 6 7 8 9 10 11
          array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • log_lik
          (chain, draw, school)
          float64
          -4.842 -3.335 ... -3.247 -3.811
          array([[[-4.84246, -3.33535, -3.81807, ..., -3.79545, -3.8976 ,
                   -3.90403],
                  [-4.08573, -3.39518, -4.33029, ..., -4.70812, -3.24862,
                   -3.83473],
                  [-5.65746, -3.31897, -3.73916, ..., -3.3867 , -4.67451,
                   -3.93941],
                  ...,
                  [-3.91769, -3.4087 , -4.06842, ..., -3.41288, -4.09026,
                   -3.81017],
                  [-5.02336, -3.40547, -3.75872, ..., -3.32613, -4.14952,
                   -3.90734],
                  [-3.75696, -3.60918, -3.7398 , ..., -3.37642, -3.61681,
                   -3.91745]],
          
                 [[-4.28416, -3.72053, -3.70102, ..., -3.31952, -4.11933,
                   -3.96637],
                  [-4.73721, -3.24968, -3.95358, ..., -3.63369, -3.42959,
                   -3.81427],
                  [-4.65488, -3.26358, -3.7822 , ..., -3.38741, -3.96876,
                   -3.87122],
                  ...,
                  [-4.17584, -3.4124 , -4.02633, ..., -3.6383 , -3.52281,
                   -3.81661],
                  [-5.43877, -3.61404, -3.71539, ..., -3.31986, -4.91245,
                   -4.02313],
                  [-5.19954, -3.40612, -3.75985, ..., -3.33871, -4.33893,
                   -3.95896]],
          
                 [[-4.10169, -3.23551, -3.69393, ..., -3.31839, -3.22389,
                   -4.09334],
                  [-5.0243 , -3.2547 , -3.706  , ..., -3.32259, -3.85061,
                   -3.98388],
                  [-4.4373 , -3.2239 , -4.01809, ..., -3.58481, -3.5196 ,
                   -3.82259],
                  ...,
                  [-5.33196, -3.56203, -3.70417, ..., -3.35482, -5.26949,
                   -3.97177],
                  [-4.48375, -3.22703, -3.77854, ..., -3.50345, -3.22186,
                   -4.04669],
                  [-4.85549, -3.27886, -3.78925, ..., -3.4397 , -3.66416,
                   -3.95239]],
          
                 ...,
          
                 [[-4.61557, -3.22682, -3.69171, ..., -3.33435, -3.69475,
                   -3.97581],
                  [-4.92917, -3.40712, -3.84876, ..., -3.33535, -4.17803,
                   -3.91566],
                  [-4.7708 , -3.22197, -3.73476, ..., -3.43421, -4.02287,
                   -3.87183],
                  ...,
                  [-6.02796, -3.65293, -4.38461, ..., -3.31689, -3.29516,
                   -3.9435 ],
                  [-5.28667, -3.54159, -3.80369, ..., -3.31753, -4.04044,
                   -3.90313],
                  [-4.02262, -3.54064, -3.81187, ..., -3.33554, -3.23887,
                   -4.17253]],
          
                 [[-4.85497, -3.28456, -3.80119, ..., -3.36636, -4.13267,
                   -3.89293],
                  [-3.91323, -4.94915, -4.22492, ..., -4.96036, -3.23148,
                   -4.35478],
                  [-4.22267, -3.24747, -3.9294 , ..., -3.575  , -3.56954,
                   -3.92078],
                  ...,
                  [-5.32923, -3.60416, -3.77723, ..., -3.32314, -4.10275,
                   -3.97869],
                  [-3.91699, -3.23201, -3.78051, ..., -3.43797, -3.36938,
                   -3.8139 ],
                  [-4.95741, -3.63518, -3.69191, ..., -3.34218, -4.19573,
                   -4.52025]],
          
                 [[-4.57723, -3.22381, -3.9008 , ..., -3.4787 , -3.79729,
                   -3.84203],
                  [-4.60246, -3.22764, -3.88173, ..., -3.46323, -3.80787,
                   -3.85568],
                  [-5.30159, -3.56015, -3.76003, ..., -3.32197, -4.81053,
                   -3.85792],
                  ...,
                  [-5.08647, -3.33452, -3.78991, ..., -3.32673, -4.16193,
                   -3.9453 ],
                  [-5.06091, -3.3648 , -3.73815, ..., -3.31739, -4.53108,
                   -3.94144],
                  [-3.83703, -3.23392, -4.50885, ..., -3.77167, -3.24699,
                   -3.81075]]])
      • created_at :
        2020-06-10T18:21:57.929618
        arviz_version :
        0.8.3

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 12
        • draw: 1000
        • chain
          (chain)
          int64
          0 1 2 3 4 5 6 7 8 9 10 11
          array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 995 996 997 998 999
          array([  0,   1,   2, ..., 997, 998, 999])
        • lp
          (chain, draw)
          float64
          -5.144 -10.34 ... -11.38 -11.14
          array([[ -5.14448, -10.3377 ,  -4.36231, ..., -11.5328 ,  -4.41412,
                   -4.53645],
                 [ -6.16728,  -7.89382,  -8.32759, ...,  -6.95914,  -8.01642,
                   -6.47187],
                 [ -4.61618,  -9.6411 ,  -6.57635, ...,  -7.53224,  -5.69699,
                   -6.2396 ],
                 ...,
                 [ -7.40979,  -8.6973 ,  -8.36134, ...,  -9.30419,  -4.65713,
                   -9.11054],
                 [ -9.35431,  -9.76551,  -7.86183, ...,  -7.19184,  -5.21445,
                   -7.71352],
                 [-10.2665 , -13.9631 ,  -9.83918, ..., -13.5776 , -11.3765 ,
                  -11.145  ]])
        • accept_stat
          (chain, draw)
          float64
          1.0 0.4431 0.9951 ... 0.9886 0.429
          array([[1.      , 0.44315 , 0.995054, ..., 0.847876, 0.887551, 0.924468],
                 [0.714286, 0.977521, 0.724435, ..., 0.934922, 0.946572, 1.      ],
                 [1.      , 0.426264, 0.992927, ..., 0.860845, 0.996249, 0.129366],
                 ...,
                 [0.892384, 0.952504, 0.999717, ..., 0.981023, 0.945826, 0.627332],
                 [1.      , 0.997771, 0.14691 , ..., 1.      , 1.      , 0.459213],
                 [0.714025, 0.911832, 1.      , ..., 0.823447, 0.988555, 0.428968]])
        • stepsize
          (chain, draw)
          float64
          0.5095 0.5095 ... 0.4323 0.4323
          array([[0.509501, 0.509501, 0.509501, ..., 0.509501, 0.509501, 0.509501],
                 [0.531567, 0.531567, 0.531567, ..., 0.531567, 0.531567, 0.531567],
                 [0.449446, 0.449446, 0.449446, ..., 0.449446, 0.449446, 0.449446],
                 ...,
                 [0.466926, 0.466926, 0.466926, ..., 0.466926, 0.466926, 0.466926],
                 [0.50536 , 0.50536 , 0.50536 , ..., 0.50536 , 0.50536 , 0.50536 ],
                 [0.432263, 0.432263, 0.432263, ..., 0.432263, 0.432263, 0.432263]])
        • treedepth
          (chain, draw)
          int64
          3 3 3 3 3 3 3 3 ... 3 3 3 3 3 3 3 3
          array([[3, 3, 3, ..., 3, 3, 3],
                 [3, 3, 3, ..., 3, 3, 3],
                 [3, 3, 3, ..., 3, 3, 3],
                 ...,
                 [3, 3, 3, ..., 3, 3, 3],
                 [3, 3, 3, ..., 3, 3, 3],
                 [3, 3, 3, ..., 3, 3, 3]])
        • n_leapfrog
          (chain, draw)
          int64
          7 7 7 7 7 7 7 ... 15 7 7 15 7 15 7
          array([[ 7,  7,  7, ...,  7,  7,  7],
                 [ 7,  7,  7, ...,  7,  7,  7],
                 [ 7,  7,  7, ...,  7,  7,  7],
                 ...,
                 [ 7,  7,  7, ...,  7,  7,  7],
                 [ 7,  7,  7, ...,  7,  7,  7],
                 [15, 15,  7, ...,  7, 15,  7]])
        • diverging
          (chain, draw)
          bool
          False False False ... False False
          array([[False, False, False, ..., False, False, False],
                 [False, False, False, ..., False, False, False],
                 [False, False, False, ..., False, False, False],
                 ...,
                 [False, False, False, ..., False, False, False],
                 [False, False, False, ..., False, False, False],
                 [False, False, False, ..., False, False, False]])
        • energy
          (chain, draw)
          float64
          9.305 15.49 12.04 ... 20.86 22.16
          array([[ 9.30492, 15.4901 , 12.0411 , ..., 14.2758 , 13.6856 ,  8.80269],
                 [15.0915 , 10.4001 , 15.2596 , ..., 13.6399 , 11.9889 , 10.6035 ],
                 [ 8.96043, 15.8938 , 13.3229 , ..., 11.9587 , 11.6787 , 11.3581 ],
                 ...,
                 [12.3025 , 16.388  , 10.6192 , ..., 19.1564 , 12.9302 , 13.1066 ],
                 [14.6137 , 11.6894 , 14.2455 , ...,  9.98162,  9.17208, 15.7546 ],
                 [19.118  , 19.03   , 16.7125 , ..., 18.6839 , 20.8571 , 22.1571 ]])
      • created_at :
        2020-06-10T18:21:57.892823
        arviz_version :
        0.8.3

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • school: 8
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • y
          (school)
          float64
          28.0 8.0 -3.0 7.0 ... 1.0 18.0 12.0
          array([28.,  8., -3.,  7., -1.,  1., 18., 12.])

From NumPyro

[18]:
import numpyro
import numpyro.distributions as dist

from jax.random import PRNGKey
from numpyro.distributions.transforms import AffineTransform
from numpyro.infer import MCMC, NUTS, Predictive

numpyro.set_host_device_count(4)

eight_school_data = {
    "J": 8,
    "y": np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]),
    "sigma": np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]),
}


def model(J, sigma, y=None):
    mu = numpyro.sample("mu", dist.Normal(0, 5))
    tau = numpyro.sample("tau", dist.HalfCauchy(5))
    # use non-centered reparameterization
    theta = numpyro.sample(
        "theta",
        dist.TransformedDistribution(
            dist.Normal(np.zeros(J), 1), AffineTransform(mu, tau)
        ),
    )
    numpyro.sample("y", dist.Normal(theta, sigma), obs=y)


kernel = NUTS(model)
mcmc = MCMC(
    kernel, num_warmup=500, num_samples=500, num_chains=4, chain_method="parallel"
)
mcmc.run(PRNGKey(0), **eight_school_data, extra_fields=["num_steps", "energy"])
posterior_samples = mcmc.get_samples()
posterior_predictive = Predictive(model, posterior_samples).get_samples(
    PRNGKey(1), eight_school_data["J"], eight_school_data["sigma"]
)
prior = Predictive(model, num_samples=500).get_samples(
    PRNGKey(2), eight_school_data["J"], eight_school_data["sigma"]
)

numpyro_data = az.from_numpyro(
    mcmc,
    prior=prior,
    posterior_predictive=posterior_predictive,
    coords={"school": np.arange(eight_school_data["J"])},
    dims={"theta": ["school"]},
)
numpyro_data
[18]:
arviz.InferenceData
    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • chain: 4
        • draw: 500
        • school: 8
        • chain
          (chain)
          int64
          0 1 2 3
          array([0, 1, 2, 3])
        • draw
          (draw)
          int64
          0 1 2 3 4 5 ... 495 496 497 498 499
          array([  0,   1,   2, ..., 497, 498, 499])
        • school
          (school)
          int64
          0 1 2 3 4 5 6 7
          array([0, 1, 2, 3, 4, 5, 6, 7])
        • mu
          (chain, draw)
          float32
          6.166989 2.7369356 ... 9.431458
          array([[ 6.166989  ,  2.7369356 ,  2.1588428 , ...,  6.5650163 ,
                   5.814288  ,  6.303744  ],
                 [ 2.8813796 ,  3.1015737 , -2.971782  , ...,  7.901584  ,
                   5.5904655 ,  3.820075  ],
                 [ 4.4399405 ,  3.5229487 ,  4.7380314 , ...,  4.63695   ,
                   5.5588846 ,  4.214654  ],
                 [ 2.9703684 ,  7.247639  ,  5.399694  , ...,  6.5445914 ,
                   0.01686172,  9.431458  ]], dtype=float32)
        • tau
          (chain, draw)
          float32
          5.4749303 2.1342402 ... 3.415198
          array([[ 5.4749303 ,  2.1342402 ,  1.4905648 , ...,  0.6671672 ,
                   0.01560028,  3.767334  ],
                 [ 7.9672894 ,  1.9319502 ,  3.1295881 , ...,  3.3490183 ,
                   3.566799  ,  0.39580163],
                 [ 2.9399393 ,  0.8484044 ,  0.9808714 , ..., 12.281746  ,
                   3.0598812 ,  1.0038422 ],
                 [ 2.0114977 ,  5.334565  ,  1.9803979 , ...,  3.915938  ,
                   3.9908662 ,  3.415198  ]], dtype=float32)
        • theta
          (chain, draw, school)
          float32
          16.805418 -0.4041652 ... 17.367815
          array([[[16.805418  , -0.4041652 , 10.278544  , ...,  2.0133018 ,
                   13.142075  , -1.8940724 ],
                  [ 3.6209416 ,  3.1639988 ,  1.6559362 , ...,  2.4664128 ,
                    6.275565  ,  1.0073171 ],
                  [ 1.2831185 ,  5.583411  ,  0.20982249, ...,  2.8672376 ,
                    5.6300173 ,  1.1305914 ],
                  ...,
                  [ 6.709765  ,  5.6444373 ,  7.9816885 , ...,  6.525248  ,
                    5.5084763 ,  6.2359204 ],
                  [ 5.8305526 ,  5.813201  ,  5.782455  , ...,  5.8331804 ,
                    5.8262672 ,  5.811961  ],
                  [ 8.371107  , 11.589505  ,  9.060078  , ...,  4.6326632 ,
                    1.3204055 ,  7.447564  ]],
          
                 [[-4.3268466 , -2.834298  , 11.134604  , ..., -1.2839447 ,
                    5.2278867 , -0.5356959 ],
                  [ 4.1689734 ,  3.332209  ,  3.7361689 , ...,  1.9161823 ,
                    3.8028543 ,  1.2852622 ],
                  [ 1.6108382 , -7.1452627 , -5.777302  , ..., -2.2040584 ,
                   -6.143371  ,  1.8476825 ],
                  ...,
                  [ 7.361441  ,  3.9002452 , 12.900136  , ...,  3.5904365 ,
                   10.234819  ,  3.1974564 ],
                  [ 5.5063396 ,  0.2793099 ,  6.444799  , ..., -1.9202161 ,
                    8.611025  ,  3.3831234 ],
                  [ 3.822883  ,  4.4135537 ,  3.6441824 , ...,  4.56769   ,
                    3.6770089 ,  3.9032135 ]],
          
                 [[ 4.00368   ,  4.4397383 ,  2.1432772 , ...,  3.1928446 ,
                    9.629471  ,  0.2643633 ],
                  [ 5.3469725 ,  4.1594777 ,  4.1849327 , ...,  4.206007  ,
                    3.4596717 ,  5.352148  ],
                  [ 4.9827085 ,  4.9556437 ,  5.1834702 , ...,  4.9021826 ,
                    5.2538424 ,  5.22963   ],
                  ...,
                  [23.39281   , 11.0239935 ,  2.3864892 , ..., 19.603878  ,
                    7.0562177 , 28.357275  ],
                  [12.852495  ,  7.4070935 ,  6.4908056 , ...,  4.894183  ,
                    5.987565  , 12.377623  ],
                  [ 6.6452794 ,  4.0932536 ,  4.729209  , ...,  4.225301  ,
                    5.1019716 ,  6.3453903 ]],
          
                 [[ 5.697102  , -0.57697064,  2.8015194 , ...,  1.3781468 ,
                    5.9575944 ,  3.632262  ],
                  [ 1.3295926 , 16.460413  ,  6.624054  , ..., 12.021828  ,
                    2.2984443 ,  7.451837  ],
                  [ 5.7512455 ,  9.078475  ,  5.3366947 , ...,  7.0837646 ,
                    6.127603  ,  5.8320184 ],
                  ...,
                  [ 8.820778  , 10.835063  ,  4.7786245 , ...,  7.6410575 ,
                    7.70269   , 12.206308  ],
                  [ 4.2434716 , -0.6336682 ,  1.3472003 , ...,  0.5414262 ,
                    4.824705  , -3.4849732 ],
                  [ 7.340993  ,  9.233242  ,  5.346336  , ...,  7.6068907 ,
                    6.1541667 , 17.367815  ]]], dtype=float32)
      • created_at :
        2020-06-10T18:22:23.947028
        arviz_version :
        0.8.3
        inference_library :
        numpyro
        inference_library_version :
        0.2.3

    • Show/Hide data repr Show/Hide attributes