ArviZ Quickstart

[1]:
import arviz as az
import numpy as np
[2]:
# ArviZ ships with style sheets!
az.style.use("arviz-darkgrid")

Get started with plotting

ArviZ is designed to be used with libraries like PyStan and PyMC3, but works fine with raw numpy arrays.

[3]:
az.plot_posterior(np.random.randn(100_000));
../_images/notebooks_Introduction_4_0.png

Plotting a dictionary of arrays, ArviZ will interpret each key as the name of a different random variable. Each row of an array is treated as an independent series of draws from the variable, called a chain. Below, we have 10 chains of 50 draws, each for four different distributions.

[4]:
size = (10, 50)
az.plot_forest(
    {
        "normal": np.random.randn(*size),
        "gumbel": np.random.gumbel(size=size),
        "student t": np.random.standard_t(df=6, size=size),
        "exponential": np.random.exponential(size=size),
    }
);
../_images/notebooks_Introduction_6_0.png

Plotting with PyMC3 objects

ArviZ is designed to work well with high dimensional, labelled data. Consider the eight schools model, which roughly tries to measure the effectiveness of SAT classes at eight different schools. To show off ArviZ’s labelling, let’s give the schools the names of a different eight schools.

This model is small enough to write down, is hierarchical, uses labelling, and a centered parameterization causes divergences (which are interesting for illustration):

[5]:
import pymc3 as pm

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])
schools = np.array(
    [
        "Choate",
        "Deerfield",
        "Phillips Andover",
        "Phillips Exeter",
        "Hotchkiss",
        "Lawrenceville",
        "St. Paul's",
        "Mt. Hermon",
    ]
)
[6]:
with pm.Model() as centered_eight:
    mu = pm.Normal("mu", mu=0, sd=5)
    tau = pm.HalfCauchy("tau", beta=5)
    theta = pm.Normal("theta", mu=mu, sd=tau, shape=J)
    obs = pm.Normal("obs", mu=theta, sd=sigma, observed=y)

    # This pattern is useful in PyMC3
    prior = pm.sample_prior_predictive()
    centered_eight_trace = pm.sample()
    posterior_predictive = pm.sample_posterior_predictive(centered_eight_trace)
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [theta, tau, mu]
100.00% [2000/2000 00:09<00:00 Sampling 2 chains, 28 divergences]
There were 8 divergences after tuning. Increase `target_accept` or reparameterize.
There were 20 divergences after tuning. Increase `target_accept` or reparameterize.
The acceptance probability does not match the target. It is 0.7010749464965044, but should be close to 0.8. Try to increase the number of tuning steps.
The rhat statistic is larger than 1.05 for some parameters. This indicates slight problems during sampling.
The estimated number of effective samples is smaller than 200 for some parameters.
100.00% [1000/1000 00:01<00:00]

Most ArviZ functions work fine with trace objects from PyMC3:

[7]:
az.plot_autocorr(centered_eight_trace, var_names=["mu", "tau"]);
/Users/percy/anaconda3/envs/arviz/lib/python3.6/site-packages/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.
  FutureWarning,
../_images/notebooks_Introduction_11_1.png

Convert to InferenceData

For much more powerful querying, analysis and plotting, we can use built-in ArviZ utilities to convert PyMC3 objects to xarray datasets. Note we are also giving some information about labelling.

ArviZ is built to work with InferenceData, and the more groups it has access to, the more powerful analyses it can perform. See the InferenceData structure specification here. Here is a plot of the trace, which is common in PyMC3 workflows. Note the intelligent labels.

[8]:
data = az.from_pymc3(
    trace=centered_eight_trace,
    prior=prior,
    posterior_predictive=posterior_predictive,
    model=centered_eight,
    coords={"school": schools},
    dims={"theta": ["school"], "obs": ["school"]},
)
data
[8]:
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)
          <U16
          'Choate' ... 'Mt. Hermon'
          array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
                 'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype='<U16')
        • mu
          (chain, draw)
          float64
          3.512 7.019 6.928 ... 8.932 6.556
          array([[ 3.51195785e+00,  7.01917337e+00,  6.92779794e+00,
                   6.47569990e+00,  8.08536381e+00,  2.19365969e+00,
                   3.65244232e+00,  2.20505112e+00,  5.91729285e+00,
                   6.26127520e+00,  6.45827158e+00,  3.76748312e+00,
                   7.11316411e+00,  8.14176645e+00,  6.73415756e+00,
                   4.68266916e+00,  5.23938322e+00,  5.95952464e+00,
                   1.52444456e+00,  8.72324149e+00,  6.30506482e+00,
                   3.80944648e+00,  3.61642865e+00,  4.61235548e-01,
                   5.22961000e+00,  6.03880910e+00,  2.60322966e+00,
                   4.98563058e+00,  2.19151534e+00,  5.12087882e+00,
                   5.94707603e+00,  9.31427437e+00,  4.32672371e+00,
                   3.58377338e+00,  3.13419921e+00,  1.69562648e+00,
                  -6.27103296e-01,  8.69385414e-01,  5.45361787e+00,
                   5.34006719e+00,  6.21134880e+00,  8.42104639e-01,
                   1.20280074e+00,  2.67233434e+00,  1.31463216e-02,
                   1.72743667e+00,  3.52052102e-01,  3.75288451e+00,
                   1.39502520e+00,  4.47969124e+00,  6.83072765e+00,
                   7.59733027e+00, -1.93159299e+00, -3.51396602e+00,
                   4.04944599e+00,  8.72322935e+00,  3.04455129e+00,
                   3.40274637e+00,  3.38480866e+00,  1.22596514e+00,
                   5.20533178e+00,  5.44063535e+00,  7.13444426e+00,
                   4.89426435e+00,  5.83544428e+00,  5.58348782e+00,
                   5.36811450e+00,  6.40725144e+00,  5.45007971e+00,
                   1.11964277e+01,  7.90820912e+00,  9.43406336e+00,
                   1.36960243e+00,  1.48985239e+00,  2.76268198e+00,
                   2.30960648e+00,  2.03965817e+00,  6.88195912e-01,
                   1.00079345e+00,  1.87923033e+00,  5.37278201e-01,
                   1.89643112e+00, -3.49860632e+00, -1.51097794e+00,
                   2.23300763e+00, -1.12660306e+00,  4.37294486e+00,
                   8.50743753e-02,  2.70058404e+00,  9.98875217e+00,
                   5.78745248e+00,  2.36137812e+00,  6.91642548e+00,
                   3.23450264e+00,  3.12976357e+00,  3.28381858e+00,
                   2.17308963e+00,  1.56571699e+00, -9.55507438e-02,
                   2.14306915e-01,  2.00763583e+00,  4.11377390e+00,
                   2.21128017e+00,  3.79102599e+00,  7.25633386e+00,
                   8.25827150e+00,  8.04694636e+00,  9.83133752e+00,
                   7.95777841e+00,  7.67583003e+00,  9.28392580e+00,
                   7.87419851e+00,  8.76189084e+00,  8.89144437e+00,
                   8.89144437e+00,  8.89144437e+00,  9.93634052e+00,
                   8.26409781e+00,  6.92072258e+00,  2.04297379e+00,
                   3.90393683e-02,  4.06630975e+00,  1.66389357e+00,
                   2.11649112e+00,  3.27684657e+00,  1.57880888e+00,
                  -1.16317379e+00,  1.10752445e+01,  1.32724595e+01,
                   9.08382451e+00,  1.14183996e+01,  3.87515263e+00,
                   3.76669799e+00,  3.66306049e+00, -3.20007212e+00,
                   6.06185747e+00,  7.04140404e+00,  6.59297569e+00,
                   7.86777425e+00,  7.13396583e+00,  4.39782496e+00,
                   4.72162074e+00,  4.72162074e+00,  4.72162074e+00,
                   4.72162074e+00,  4.72162074e+00,  5.09803930e+00,
                   4.69606443e+00,  4.69606443e+00,  4.69606443e+00,
                   4.26456141e+00,  4.97933289e+00,  4.97933289e+00,
                   4.97933289e+00,  1.21591864e+00, -1.16144258e+00,
                   2.26910138e+00,  1.28394440e+00, -1.37271634e+00,
                   3.93312931e+00,  2.84273164e+00, -3.11707638e-01,
                  -5.87394446e-01, -5.84303443e-01,  1.74997031e-01,
                   9.61091861e-01,  5.31615139e+00,  5.48102034e+00,
                  -1.69506328e+00,  6.03575011e+00, -3.24626526e+00,
                   4.26654687e+00,  4.96572775e+00,  5.94403492e+00,
                   2.17234873e-01, -6.17444514e-01, -1.88166146e+00,
                   2.54682033e+00,  4.22087318e+00,  5.00202927e+00,
                   1.71673395e+00,  9.14486494e+00,  8.56546264e+00,
                   8.96110726e+00,  6.81906700e+00,  6.58674268e+00,
                   5.34652335e+00,  6.29929616e+00,  6.77577574e+00,
                   5.48215683e+00, -8.90156161e-01,  5.42252687e+00,
                   3.67234154e+00,  7.57719031e+00,  7.67514108e+00,
                   2.91224227e+00,  6.03711427e-01,  5.00421045e+00,
                  -4.51011712e+00,  6.62131067e+00,  4.00823882e+00,
                   1.52157756e+00,  5.34224927e+00, -7.43534705e-01,
                   7.23068677e+00,  3.56319789e+00,  4.24199339e+00,
                   4.66494333e+00,  3.55428570e+00,  2.36397658e+00,
                   2.83246370e+00,  5.47089122e+00,  5.43433201e+00,
                   8.01070301e+00,  1.39405227e+01,  6.57251236e+00,
                   4.95607031e-01,  4.83590271e+00,  4.94076987e+00,
                   6.60425903e+00,  9.91608232e+00,  8.87384097e+00,
                   6.87554783e+00,  5.22623548e+00,  1.49783921e+00,
                   1.31781090e+00,  4.26263902e+00,  4.06934357e+00,
                   4.51604168e+00,  4.51604168e+00,  5.33345347e+00,
                   4.75484094e+00,  4.87396423e+00,  4.46413123e+00,
                   3.77005516e+00,  8.50333312e+00,  8.52377148e+00,
                   1.95148205e+00,  1.95148205e+00,  1.95148205e+00,
                   1.95148205e+00,  8.87558786e-01,  6.77794554e-01,
                   6.77794554e-01,  6.00683581e-01,  6.00683581e-01,
                   2.13140444e-01,  2.13140444e-01,  9.62265948e-01,
                   9.62265948e-01,  9.62265948e-01,  9.62265948e-01,
                   2.97369250e+00,  3.50295664e+00,  3.16138578e+00,
                   2.71607305e+00,  3.21430781e+00,  4.68108975e+00,
                   5.39371584e+00,  4.36365013e+00,  3.44272240e+00,
                   3.91766939e+00,  3.70744867e+00,  1.95595388e+00,
                   6.45637370e+00,  2.66820407e+00, -1.92000240e+00,
                   2.01574705e+00,  5.07342363e+00,  5.95953196e+00,
                   1.06286793e+01,  3.03180019e+00,  4.33542234e+00,
                   4.86430851e+00,  5.09336171e+00,  2.87811963e+00,
                   2.36616982e+00,  8.02265475e+00,  8.66260046e+00,
                   1.05811553e+01,  1.18033548e+01,  8.63657997e+00,
                   9.78998008e+00,  6.26635678e+00,  1.69416863e-01,
                   5.07612933e+00,  2.86740313e+00,  4.74653352e+00,
                   4.52618655e+00,  6.00697279e+00,  8.62581056e+00,
                   8.57315100e+00,  4.72435226e+00,  4.93482055e+00,
                   4.38356401e+00,  4.38356401e+00,  4.38356401e+00,
                   4.64407367e+00,  4.64407367e+00,  4.64407367e+00,
                   4.64407367e+00,  4.64407367e+00,  4.64407367e+00,
                   4.64407367e+00, -1.78807313e-01,  2.00835318e-01,
                   1.17248826e+00,  1.84052770e+00, -1.08044972e+00,
                  -1.71491637e-01,  3.32121366e-01,  3.00561296e+00,
                   1.37570672e+00, -1.87959878e+00,  9.43675234e+00,
                   9.32607570e+00,  7.72867728e+00,  8.05238969e+00,
                   6.58593550e+00,  8.66364708e+00,  6.40927983e-01,
                   2.63983672e+00,  3.76701325e+00,  2.82875578e+00,
                  -8.12305621e-01, -3.70638166e-01,  2.99626655e+00,
                   1.03874142e+00, -9.70996839e-01, -3.02481420e-02,
                   3.72899909e+00,  6.90916567e-01,  2.51671358e-01,
                   6.98517362e+00,  8.96852245e+00,  1.62305398e+00,
                   4.04879654e+00,  1.73106825e+00,  3.66782317e+00,
                  -1.18863732e+00,  8.20205261e+00,  5.41949482e+00,
                   2.91441912e-01,  4.41035967e-01,  4.42943465e+00,
                   4.89252792e+00,  1.15716057e+01,  8.10099451e+00,
                   3.53121976e+00,  1.81494404e+00,  9.06956925e-01,
                   6.15425925e+00,  1.06653458e+00,  9.37849490e+00,
                   1.14684574e+01,  7.81328215e+00,  9.98694886e+00,
                   6.15833217e+00,  1.82070341e+00, -3.43318137e-01,
                   6.36850297e+00,  2.17093702e-01,  3.87395330e-01,
                  -5.14314067e-02, -5.84877149e-01,  5.02831559e+00,
                   7.22030063e+00,  5.71884405e+00,  5.71884405e+00,
                   3.24733550e+00,  2.01359745e+00,  1.54234893e+00,
                   4.24279230e+00, -8.00968058e-02,  1.35462439e+00,
                   3.93613538e+00,  5.62515672e+00,  2.96637541e+00,
                  -2.59581160e+00,  6.12731394e-01, -1.04756914e+00,
                   6.71141722e+00,  8.65737175e+00, -3.01857240e+00,
                   1.12181979e+01, -2.83072057e+00,  7.16086220e+00,
                   3.25962309e+00,  8.18953089e+00,  6.86712365e+00,
                   2.59079254e+00,  2.80862970e+00,  3.59865591e+00,
                   2.66772270e+00,  2.40397494e+00, -6.42691274e-01,
                   1.34168497e+00,  3.88796281e+00,  6.25804261e+00,
                   6.44287617e+00,  7.45914976e+00,  5.55156569e+00,
                   5.42579521e+00,  4.29802502e+00,  4.41741044e+00,
                   4.41741044e+00,  4.98872974e+00,  5.48756383e+00,
                   2.37522403e+00,  1.29066114e-01,  2.95794341e+00,
                   2.90498367e+00,  2.77415055e+00,  3.25153129e+00,
                   1.18308912e+00,  1.53329682e+00,  3.05230571e+00,
                   1.85861885e+00, -1.43830341e+00, -1.90380940e+00,
                   1.57341737e+00,  1.84685715e+00,  8.76211188e+00,
                   9.75419351e+00,  1.25098763e+00,  5.31840090e+00,
                   1.00938181e+01,  4.95378567e+00,  7.73426026e+00,
                   2.93918646e+00,  3.90206598e+00,  4.75598702e+00,
                   8.30461646e-01,  1.41428696e+00,  9.07643223e-01,
                   1.42609835e+00,  2.59269257e+00, -2.26240581e+00,
                   4.36989451e+00,  5.41240986e+00,  4.17274850e+00,
                   3.21178400e+00,  1.62681872e+00, -2.53387822e+00,
                   3.96394985e+00,  5.80280832e+00,  5.89032858e-01,
                   2.26615891e+00,  2.65647539e+00,  3.73538916e+00,
                   6.87534241e+00,  3.78122790e+00,  3.92859490e+00,
                   5.36292708e+00,  3.85109972e+00,  7.89796134e+00,
                   9.04076879e+00,  6.52376621e-01,  1.44256542e+00,
                   3.74719085e+00,  5.30433433e+00,  3.44604007e+00,
                   9.43717210e+00,  7.25491521e+00,  7.87818305e+00,
                   5.36477886e+00,  1.10255199e+01,  4.18706868e+00,
                   6.78741581e+00,  7.77967454e-01,  1.60550446e+00,
                   4.80386104e+00,  8.33117640e+00,  9.37993395e+00,
                   7.37533539e+00,  8.04145210e+00,  5.36724133e+00,
                   1.23069113e+00,  9.83509603e-01, -3.88820770e-02,
                   8.58583687e+00,  6.40925005e+00,  3.50227902e+00,
                   1.22653340e+00,  3.81713450e+00,  1.40827111e+00,
                   7.49308946e+00,  7.91922367e+00, -3.14975497e+00,
                  -4.10526791e+00,  4.45725519e+00,  5.56758696e+00,
                   2.52942919e+00,  9.15189492e+00,  8.19637975e+00,
                   5.66618613e+00,  7.66371704e+00,  6.47419205e+00,
                   6.47419205e+00,  5.75140344e+00],
                 [ 1.01125830e+01,  1.01352607e+01,  1.01352607e+01,
                   1.01352607e+01,  9.84539952e+00,  9.74913284e+00,
                   9.09325291e+00,  1.01827502e+01,  8.51901288e+00,
                   8.48307996e+00, -1.05102753e+00,  2.44009863e+00,
                   1.41244986e+00,  8.58725000e-01,  8.31563489e+00,
                  -1.45316766e+00, -1.74115953e+00,  2.61985464e+00,
                   6.61707078e+00, -4.48859445e+00, -7.81725226e-01,
                   5.28967135e+00,  4.27625977e+00, -2.40249910e-02,
                   1.62456000e+00,  2.06047397e+00, -7.83182849e-01,
                  -3.07703445e-01,  2.07808735e+00,  2.25993518e+00,
                   4.97002864e+00,  3.21510356e+00,  5.45299985e-01,
                  -1.01573957e-01,  6.42787497e+00,  6.57437655e+00,
                   8.35827360e+00,  8.33947896e+00,  9.17250258e+00,
                   8.49908228e+00,  8.80032679e+00,  7.37727304e+00,
                   8.71856036e+00,  8.70127770e+00,  8.76383110e+00,
                   1.01796431e+01,  8.78975935e+00,  7.50344824e+00,
                   1.10863497e+01,  3.16771776e+00,  3.33947979e+00,
                   4.10947735e+00,  4.06653306e+00,  6.21084345e+00,
                   4.22150394e+00,  4.16511137e+00,  1.11054786e+01,
                   5.78891226e+00,  5.76900478e+00,  8.96605464e+00,
                   9.63748287e+00,  1.07423114e+01,  3.67629405e+00,
                  -1.84402332e+00,  1.51140764e+00,  4.53998953e+00,
                   5.49010094e+00,  6.56136808e+00,  7.51268539e+00,
                   7.08915416e+00,  5.74437822e+00,  5.34983638e+00,
                   4.55526368e+00,  6.03479856e+00,  7.56353426e+00,
                   4.07692163e+00,  4.53400935e+00,  2.19593015e+00,
                   7.97723920e+00,  7.10899569e+00, -2.04042453e-01,
                   7.90978418e-01,  3.76501450e+00,  6.99469608e+00,
                   5.31022948e+00, -3.04494394e+00,  2.04323864e+00,
                   7.24051476e-01, -5.53505494e-01,  1.40472319e+00,
                   3.86812324e+00,  6.34015250e+00,  3.58003954e+00,
                   3.45266999e+00,  8.16165159e-01,  1.71082218e+00,
                   3.81392244e-01,  1.41119882e+00,  2.60608746e-01,
                  -7.66088086e-01, -1.13674537e+00,  1.62428777e+00,
                  -1.98907214e-01,  1.09495059e+00, -1.04071549e+00,
                   2.43808556e+00,  2.20974521e+00,  2.70699932e+00,
                   4.13640558e+00,  3.55890753e+00, -4.44999462e-02,
                  -4.32892501e-01, -1.53471422e+00, -8.56425210e-01,
                  -3.79402867e+00, -3.02159344e+00,  3.42965880e+00,
                   9.62124626e-01,  9.62124626e-01,  1.04810241e+01,
                   1.03985338e+01,  1.02297222e+01,  7.99905519e+00,
                   5.19305256e+00,  4.82432763e+00,  5.34330335e+00,
                   4.66272490e+00,  4.30724952e+00,  5.17055236e+00,
                   4.72806880e+00,  5.97495027e-02,  3.41639829e+00,
                   3.77399321e+00,  6.81831739e+00,  2.33082034e+00,
                   4.32519379e+00,  4.16851588e+00,  4.00601934e+00,
                   6.57172483e+00,  3.29197375e+00,  3.33636860e+00,
                  -5.57334960e-01,  1.65254362e+00,  1.76170591e-01,
                   1.95164852e+00, -7.88119197e-02, -2.09289252e+00,
                  -5.38001047e-01,  9.93993698e+00,  1.48824506e+00,
                   7.30162274e+00, -2.72009315e+00,  4.83293831e+00,
                   5.23641033e+00,  7.16493772e+00,  3.27435914e+00,
                   3.40984096e+00,  6.66932369e+00,  5.85026018e+00,
                   6.30968991e+00,  6.67838245e+00,  6.62609730e+00,
                   8.68632794e+00,  4.71664570e+00,  6.56547486e+00,
                   6.60164205e+00,  2.55822347e+00,  6.93057743e+00,
                   8.64702538e+00,  6.62824036e+00,  5.73548470e-01,
                   2.96003138e+00,  2.89824883e+00,  2.82957241e+00,
                   2.27510900e+00, -2.04834091e+00,  4.99673580e+00,
                   7.30432097e+00,  8.64154272e+00,  9.44653181e+00,
                   9.07297437e-01,  2.78768748e-01,  2.49164351e+00,
                   6.95557818e+00,  1.23269136e+00,  8.72467726e+00,
                   5.75550981e+00,  3.62101955e+00,  1.84344777e+00,
                   6.31967858e+00,  3.90558797e+00,  2.54156004e+00,
                   5.30132016e+00,  1.49674849e+00,  6.41388961e+00,
                   4.60677424e+00,  4.60677424e+00,  4.81986321e+00,
                   4.81986321e+00,  6.81902038e+00,  2.83566809e+00,
                   3.30156169e+00,  6.45109445e-01,  4.07393865e+00,
                   1.18952825e+00,  1.62245439e+00,  8.98719437e-01,
                   8.76664829e+00,  7.12406693e+00,  8.11650568e+00,
                   9.51335924e+00,  1.50124329e+00,  9.69975312e+00,
                   4.50114740e+00,  6.23839250e+00,  5.30152304e+00,
                   7.88676354e+00,  5.06772128e+00,  6.95126935e+00,
                   4.91561679e+00,  1.78928842e+00,  5.17148441e+00,
                   4.60694929e+00,  5.49798646e+00,  5.78833098e+00,
                   5.06765579e+00,  7.03756145e+00, -1.12355522e+00,
                   8.25261797e+00,  7.08479233e+00,  8.06452210e+00,
                   9.13985843e+00,  1.30621659e+01,  1.15367276e+01,
                   1.15156736e+01,  7.59090554e+00,  1.64541574e-02,
                   4.70983875e+00,  1.64027011e+00,  2.89269830e+00,
                   2.72337694e+00,  2.72337694e+00,  2.72337694e+00,
                   2.81516687e+00,  4.55369902e+00,  3.17790374e+00,
                   3.08967805e+00,  2.92126999e+00,  5.35278202e+00,
                   1.09727582e+01,  1.20143779e+01,  7.08640745e+00,
                   8.34953776e+00,  4.22847117e+00,  7.22259634e+00,
                   6.90166195e+00,  5.23091514e+00,  5.59950203e+00,
                   6.22892679e+00,  7.48779288e+00,  8.10404930e+00,
                   8.22861944e+00,  7.47933725e+00,  6.06846024e+00,
                   6.81981359e+00,  9.49349100e+00,  9.28983543e+00,
                   7.79204648e+00,  7.79204648e+00,  9.84582259e+00,
                   5.97171471e+00,  3.48002650e+00,  3.39290197e+00,
                   5.56116651e+00,  6.07466168e+00,  6.08519745e+00,
                   7.30734481e+00,  5.60950600e+00,  1.93133831e+00,
                   5.33444110e+00,  3.48678021e+00,  5.02164778e+00,
                   1.07863767e+01,  1.04997063e+01,  8.96977837e+00,
                   8.59407826e+00,  7.46429395e+00,  6.58257883e+00,
                   9.89365687e+00,  4.21364589e+00,  4.31137962e+00,
                   3.19000152e-01,  3.34490768e+00,  2.87859209e+00,
                   2.71133060e+00,  2.34387322e+00,  3.04862614e+00,
                   1.55850408e+00,  9.50076438e+00,  2.95118044e+00,
                   5.33512315e+00,  8.99567519e-01, -7.50524532e-01,
                   4.06241292e+00,  5.18395430e+00,  5.54755112e+00,
                   3.44040332e+00,  2.56137657e+00,  3.51407561e+00,
                   6.21394197e+00,  7.32583192e+00,  5.98897956e+00,
                   4.18851134e+00,  3.88469970e+00,  2.86900782e+00,
                   2.86900782e+00,  3.28746343e+00,  4.06115164e+00,
                   3.74442876e+00,  5.14727998e+00,  5.38374014e+00,
                   6.19420599e+00, -2.27737673e+00,  1.80283938e+00,
                  -5.75572719e-01, -1.24073560e+00, -1.05257156e+00,
                  -2.47835472e+00, -2.16564602e-01, -2.16564602e-01,
                  -4.11372846e-01, -4.11372846e-01, -4.11372846e-01,
                   1.14918512e-01,  1.14918512e-01,  1.14918512e-01,
                   1.14918512e-01,  2.93617779e-01,  2.93617779e-01,
                   9.22746794e-01,  2.41525739e+00,  1.76269204e+00,
                   1.08438500e+00,  2.03202613e+00,  9.04938062e-01,
                   2.41683938e+00,  1.63266773e+00,  1.33700250e+00,
                   2.93398957e-01,  5.53197303e-01, -1.77297852e+00,
                  -2.74445850e-01,  5.12472462e+00,  5.05442060e+00,
                   5.91122843e+00,  5.28340167e+00,  5.56015822e+00,
                   8.37159578e+00,  8.37159578e+00,  7.53902617e+00,
                   7.53902617e+00,  7.57398582e+00,  7.57398582e+00,
                   7.57398582e+00,  7.57398582e+00,  7.57398582e+00,
                   7.57398582e+00,  7.57398582e+00,  7.57398582e+00,
                   7.57398582e+00,  7.57398582e+00,  7.57398582e+00,
                   7.57398582e+00,  7.57398582e+00,  7.12177163e+00,
                   7.12177163e+00,  7.12177163e+00,  7.12177163e+00,
                   7.12177163e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.00271050e+00,  7.00271050e+00,
                   7.00271050e+00,  7.28918369e+00,  7.28918369e+00,
                   7.28918369e+00,  7.79406447e+00,  7.37188274e+00,
                   4.99661803e+00,  6.15600775e+00,  6.33158534e+00,
                  -2.44004724e+00, -1.41019288e+00,  6.46119482e+00,
                   7.49143600e+00,  8.66585278e+00,  7.71151541e+00,
                   9.19750914e+00,  3.15677149e+00,  2.27029450e+00,
                   4.06501115e+00,  5.42602431e+00,  5.47474935e+00,
                   4.92843005e+00,  4.10757446e+00,  9.89210184e+00,
                   1.38284992e+01,  1.08730943e+01,  1.04565129e+01,
                   7.88747336e+00,  9.57606543e+00, -1.67341575e+00,
                  -8.76106406e-01, -3.80433909e-01, -1.45107436e-01,
                   2.82789048e-01,  2.45110278e-01, -3.05020827e+00,
                  -3.64902676e-01,  3.30531018e+00,  3.43108278e+00,
                   6.42328656e+00,  7.43776480e+00,  7.01249761e+00,
                   4.56480110e+00,  4.96057858e+00,  4.50726956e+00,
                   4.92606350e+00,  4.19785477e+00,  2.37624992e+00,
                  -1.12270584e-01, -6.39096297e-02, -3.29190669e+00,
                   2.15480018e+00,  3.50166005e+00,  2.39339122e+00,
                   1.47543845e+00,  8.53976865e+00,  7.71207664e+00,
                   6.03514284e+00,  1.21351206e+01,  1.14523457e+01,
                   8.93169830e+00,  6.55633128e+00]])
        • theta
          (chain, draw, school)
          float64
          6.531 3.607 0.4764 ... 10.13 12.32
          array([[[ 6.53117908,  3.6065954 ,  0.47641283, ..., -0.92196222,
                    4.92486228,  4.03024001],
                  [ 4.82971661,  5.23241008,  8.70718583, ...,  9.02970049,
                    5.84378847,  6.00280818],
                  [12.84588154,  5.72244944,  8.09629112, ...,  7.31577128,
                    9.28315496,  6.55685548],
                  ...,
                  [ 6.22525064,  6.04614614,  5.5073631 , ...,  8.32961177,
                    5.88614179,  6.46095041],
                  [ 6.22525064,  6.04614614,  5.5073631 , ...,  8.32961177,
                    5.88614179,  6.46095041],
                  [ 6.47224282,  7.07333431,  7.23084151, ...,  4.8586215 ,
                    6.65519116,  6.4171545 ]],
          
                 [[10.61044089,  9.93823752, 11.43751424, ..., 10.98465408,
                    9.39697225, 10.85064596],
                  [ 8.57351916, 12.1206435 , 10.24247372, ...,  9.37021741,
                   10.17802814,  9.63051968],
                  [ 8.57351916, 12.1206435 , 10.24247372, ...,  9.37021741,
                   10.17802814,  9.63051968],
                  ...,
                  [16.71726571,  9.60094263, 13.71982007, ..., 14.16131649,
                   13.11647601, 18.79277735],
                  [11.88039806, 10.03600833, 12.24545544, ...,  9.29449848,
                   13.66392076, 13.12868937],
                  [ 7.58797243, 10.11726456, 14.53218427, ...,  6.64551025,
                   10.1260629 , 12.31751554]]])
        • tau
          (chain, draw)
          float64
          2.673 1.693 2.264 ... 5.256 5.096
          array([[ 2.67326225,  1.69327225,  2.26441946,  2.28373937,  2.48337685,
                   3.5534519 ,  4.59569498,  3.89443484,  6.29093191,  4.15534065,
                   5.23877865,  5.50860947,  3.80449605,  3.53618773,  3.53556815,
                   3.83213975,  2.26159133,  1.70996414,  4.30431708,  5.18004681,
                   8.44122625,  6.74853278, 11.66327816, 11.50322115,  4.64237938,
                   7.58836957,  5.41253562,  3.8259386 ,  2.42179492,  6.07911823,
                   5.7579538 ,  9.10245313,  4.24493377,  6.16846468,  9.52246892,
                   6.16850002,  6.93453894,  9.06885683,  5.23951572, 14.88285834,
                   7.61015605, 10.95611743,  8.18538236,  7.9080973 ,  8.38219843,
                   9.67272328,  8.00163612,  8.05394593, 11.70553097,  3.32828189,
                   4.91360016,  9.07209215, 12.4677597 ,  3.50645773,  3.26083374,
                   6.04138238,  4.21296333,  4.20178591,  3.0890811 ,  3.70392596,
                   3.02528969,  1.81836961,  3.37416903,  2.85952533,  4.56593347,
                   3.57947128,  3.00088854,  2.52328479,  4.38582071,  2.99649689,
                   3.15782354,  4.71241533,  2.54766776,  4.18337528,  2.20466968,
                   2.19423239,  1.95878443,  4.00996825,  3.79787455,  2.66722218,
                   1.56778782,  2.67459744,  5.6288038 ,  5.27926994,  8.08829096,
                   6.64229416,  6.32189519,  5.52907913,  8.41063894,  6.38655596,
                   6.71688517,  6.12048595,  9.5443802 ,  7.12108513,  1.7041854 ,
                   3.03242712,  1.58026182,  3.45989141,  5.73044874,  8.54773302,
                   9.93081775,  4.48757783,  3.80658091,  3.21910374,  1.74277026,
                   1.54134775,  2.34914236,  1.76723076,  3.33191492,  1.55417962,
                   1.44801848,  1.63040306,  1.77156976,  1.26546036,  1.26546036,
                   1.26546036,  2.09392397,  3.911303  ,  3.60844456,  3.06605205,
                   5.84442689,  4.76918761,  5.04368956,  5.89823556,  4.14501552,
                   4.96545057,  5.98554752,  6.16992784,  5.36074059,  5.98746562,
                   4.76558208,  3.56179071,  6.03837811,  8.18572283,  9.40440231,
                   2.22605209,  1.41750717,  2.56021681,  1.52054509,  1.25267437,
                   1.18064931,  0.82523799,  0.82523799,  0.82523799,  0.82523799,
                   0.82523799,  0.89547968,  1.06515249,  1.06515249,  1.06515249,
                   0.87941658,  0.93262386,  0.93262386,  0.93262386,  1.70245357,
                   3.56918409,  2.90302204,  4.14536914,  4.68165271,  3.8085819 ,
                   5.70169104,  5.09458127,  3.68444235,  3.07163961,  3.27855361,
                   3.37129431,  7.84295691,  5.38165233,  4.21482058, 11.01347963,
                   3.46440289,  2.33344028,  3.63233906,  6.00011695,  6.02585805,
                   4.59248514,  1.25218832,  2.4455758 ,  1.41912495,  2.40001986,
                   2.09110479,  1.76894054,  1.38091801,  1.33776424,  2.4548559 ,
                   1.47558606,  4.28803147,  2.84428473,  3.44486303,  4.81141509,
                   8.13442314,  6.38616741,  4.71908787,  6.62655314,  6.81004414,
                   3.12343065,  8.53267586,  8.60231967, 11.83721142, 10.24416421,
                   4.49721931,  8.72194144, 10.65211709,  8.54544754,  5.18207439,
                   6.82105618,  3.01369765,  3.8354013 ,  5.83414842,  5.95179166,
                   5.05889385,  3.51063938,  3.42927438, 10.37775248, 23.21470877,
                   7.4125489 ,  7.81157586,  4.41289201,  2.99479598,  2.44415618,
                  11.85146551,  2.60079037,  3.3420645 ,  2.35037452,  3.3537721 ,
                   4.49542609,  3.56641889,  1.01056969,  1.23338844,  1.23338844,
                   1.11110148,  1.20214637,  0.98375117,  1.09738411,  1.21888324,
                   1.40145365,  1.24431932,  1.04448701,  1.04448701,  1.04448701,
                   1.04448701,  0.8957644 ,  0.93776913,  0.93776913,  0.92217105,
                   0.92217105,  1.09089615,  1.09089615,  1.34084131,  1.34084131,
                   1.34084131,  1.34084131,  1.78776261,  1.56065016,  1.93324153,
                   3.12974917,  3.03156828,  3.24434882,  3.68852741,  3.46071732,
                   4.53658384,  3.21777084,  6.89241731,  5.86051587,  4.90313114,
                  13.34213779, 10.43093357,  9.8464825 ,  4.085654  ,  7.67111665,
                   3.11735387,  6.16268338, 10.0382515 ,  2.14874536,  3.22442554,
                   3.07794522,  4.2880126 ,  5.74101492,  2.17788048,  2.06063997,
                   3.08095301,  6.11589352,  3.7712119 ,  4.79790927,  7.01993216,
                   7.69613364,  3.9409763 ,  9.87253501,  3.16807662,  7.62792385,
                   2.4380227 ,  2.25244931,  1.82277843,  1.00373686,  0.96859461,
                   0.96859461,  0.96859461,  0.93270199,  0.93270199,  0.93270199,
                   0.93270199,  0.93270199,  0.93270199,  0.93270199,  2.38731884,
                   2.39693547,  2.33877376,  2.55256205,  3.20162928,  1.43372253,
                   1.55533021,  4.54687869,  3.10383668,  7.99636156,  4.34784516,
                   4.09481755,  2.79684298,  3.44660827,  2.61954456,  2.24450866,
                   4.53931356,  4.39396726,  9.04018833,  6.56933644, 12.48666978,
                  10.4613815 , 17.38898537,  9.26310989, 15.18800819,  7.78257061,
                  10.34866689,  9.80659621,  3.56739801,  2.44289005,  4.0299327 ,
                   4.02353188,  7.91856192,  3.59124329, 11.03600136, 10.67612793,
                   5.96198989,  4.31578002, 15.20539491, 14.1175014 ,  6.41326514,
                   4.41373361,  3.94972014,  3.49280734,  6.38378125,  3.72676669,
                   3.97751008,  8.09200822,  3.5869942 , 14.91109664, 11.49784435,
                   6.68131178,  2.58694806,  3.59462808,  5.08865708,  4.9357594 ,
                   2.15768411,  1.54657273,  1.83638171,  1.58362072,  1.7523732 ,
                   2.085632  ,  1.77962539,  1.44335826,  1.44335826,  2.64060866,
                   2.6804101 ,  3.06141175,  6.0021514 ,  6.75034837,  4.84780222,
                   6.28158582,  5.12052529,  8.46983638,  6.15288293,  3.52185536,
                   4.34919414,  3.82498954,  9.43059195, 17.94770233,  9.61985205,
                  10.1235112 , 12.94659851,  9.31481323,  8.44393295,  3.98696312,
                   2.73993392,  3.41901356,  4.13167884,  2.51136656,  2.93017373,
                   3.84590493,  2.8127721 ,  1.60414855,  1.73826593,  3.53341914,
                   3.75506114,  3.16055637,  1.52917217,  1.31002964,  1.17154789,
                   1.17154789,  1.72071883,  1.9681178 ,  3.50687245,  4.94258162,
                   2.63429557,  3.38741781,  3.21155739,  3.28131916,  4.39854645,
                   2.56272633,  5.78967658, 12.0968391 ,  6.89258195,  9.61183744,
                  12.1241828 , 10.1158111 ,  7.0622766 ,  7.75912659, 12.75892791,
                  10.256167  ,  8.32404926,  7.74108702,  7.44426077,  9.33724162,
                   8.44900821, 11.32260193,  5.63486066, 12.37678267,  5.49428901,
                   3.72611928,  6.33533045,  5.48278516,  4.29037045,  5.95626253,
                   5.40273459,  5.62748716,  4.82756157, 10.76529541, 10.69283667,
                  10.52683113,  4.93184524,  6.04815438,  5.03766243,  3.83245661,
                   4.30334325,  2.17109017,  2.52787927,  1.60872106,  1.33502516,
                   2.00961732,  1.99782636,  6.64058804,  4.49992205,  5.80234939,
                   2.88411343,  8.17682545,  3.24663948,  3.28604191,  5.59214365,
                   6.66206916,  5.59528906,  7.99377242,  7.89452165,  6.28027467,
                   6.16042518,  8.68820432,  6.81936392,  3.08463524,  2.52183358,
                   5.13910632,  5.79876205,  8.61744898,  5.11191357,  5.3789732 ,
                  10.43804718,  3.85422562,  5.92473426, 11.63939767,  7.00127952,
                   6.12648248,  3.16995738,  3.60015104,  6.07323179,  5.45281603,
                   8.56568605,  3.63093546,  6.42400208,  1.85250422,  2.76356095,
                   3.87937596,  2.74449388,  0.95877952,  0.95877952,  1.02231547],
                 [ 0.87446012,  0.82158698,  0.82158698,  0.82158698,  0.7899858 ,
                   0.81261676,  1.34523251,  1.23673433,  2.70381336,  2.17895614,
                   5.68064657,  8.53942839,  5.60146557,  7.92459687,  3.8407719 ,
                   9.45083314,  3.86839546,  4.84523909,  6.77770367,  8.12935539,
                   8.86591202,  7.40347762, 11.53362792,  7.70886326,  3.90921858,
                   4.19890237,  9.30457973,  8.7934137 ,  3.86291871,  3.86730112,
                   3.67796732,  2.72912066,  4.02009987,  5.90151154,  4.36799819,
                   4.12431699,  3.0169841 ,  1.76103489,  5.65498505,  1.642834  ,
                   1.48589934,  1.33171688,  2.1900742 ,  1.74737413,  2.80989782,
                   2.99299058,  3.16559515,  4.14072242,  3.42463653,  6.26443922,
                   4.26165586,  3.79951099,  4.18292099,  6.35392115,  8.18009509,
                   9.82519028,  2.35092275,  6.21469846,  4.86941576,  3.46001393,
                   2.92697617,  4.21795968,  8.69209967,  8.15649408,  4.69825256,
                   5.56048019,  2.99158626,  2.24030763,  2.40927516,  2.56021411,
                   1.79421235,  3.6365905 ,  3.75594969,  4.04357977,  4.87286547,
                   9.37538826, 14.08385188,  8.7300695 , 13.62297943, 10.10811741,
                  11.96159103, 14.31232373,  7.2746315 , 10.73875997,  6.50516768,
                   6.36908336,  6.26214526, 17.00226039, 11.69573731, 13.1200249 ,
                   6.11724095, 15.60658914,  1.95291595,  2.53914574,  2.1495062 ,
                   1.94886689,  3.26605563,  2.17701759,  2.52965815,  2.2098353 ,
                   1.94958174,  1.36302759,  5.42559586,  5.41986439, 12.17111501,
                   3.9309188 ,  4.37587659, 12.80156449,  3.62105571,  4.05579294,
                   2.96202686,  4.00137303,  3.4702907 ,  2.6269301 ,  2.77133531,
                   2.31719863,  5.12579435,  1.11033036,  1.11033036,  2.51566695,
                   2.30777883,  2.44456502,  2.71264448,  4.80757246,  2.07594995,
                   2.25283042,  5.94743906,  2.25520828,  2.40038293,  2.18351887,
                   5.54238846,  3.33618964,  3.99921708,  4.24352368,  4.91763749,
                   3.96403672,  3.0033376 ,  3.91393073,  3.62823827,  1.27425084,
                   2.05416305,  3.32391083,  4.41850247,  2.16151761,  1.93777731,
                   5.69216908,  7.96661813,  9.90702467,  7.96348674,  5.143967  ,
                  17.32222786, 12.31574761,  7.58995324,  9.54868096,  5.78418544,
                   3.47807987,  2.65905991,  4.82217952,  3.31179254,  2.35190876,
                   4.64002679,  6.57777407,  6.57764149,  4.30911656,  6.11807292,
                   5.53419999,  2.09692156,  3.49538724,  2.04720002,  8.58185636,
                   4.93869456,  5.07551233,  5.45923137,  5.66055253,  8.56854194,
                  15.39743242, 12.08606238,  7.22316086,  7.96972784,  5.1599483 ,
                   4.58556989,  4.94484151,  4.897299  ,  7.52739652,  6.04513495,
                   5.13407879,  7.14078658, 12.00053016,  9.43733288,  6.38635937,
                   6.80033707,  6.57770054,  4.45173614,  3.18899484,  2.26849151,
                   1.1416066 ,  1.1416066 ,  0.93440577,  0.93440577,  1.81729944,
                   5.03557383,  5.12429328,  2.21205836,  6.18590091, 11.19469957,
                   8.87184499,  8.88232154,  4.02002437,  5.32776175,  3.54149267,
                   4.81504989,  9.64118715,  7.89750536,  5.81875906,  7.81992102,
                   7.54916279, 10.82465269,  4.1484651 ,  3.60149111,  4.88051874,
                   5.16847133,  6.8727861 ,  5.51125077,  6.28097161,  2.75305999,
                   2.52103133, 10.29985714,  9.01125755,  8.74221341,  2.7497625 ,
                   1.95925068,  1.90946984,  2.59981888,  3.47182994,  6.23661491,
                   5.96628356,  8.84906534, 10.68528257,  5.33192173,  5.78270999,
                   1.27349183,  1.27349183,  1.27349183,  1.52474907,  2.08950004,
                   2.37422809,  2.66453157,  2.70655422,  4.5759727 ,  2.74764816,
                   4.20049562,  9.51129361,  4.28413236,  6.87610199,  5.68991202,
                   1.29607444,  2.94959754,  2.96994402,  1.56037111,  2.461318  ,
                   2.78204738,  1.43925123,  1.64512448,  2.278369  ,  2.63951027,
                   1.74140447,  1.1714692 ,  0.97316354,  0.97316354,  2.76896219,
                   3.69339381,  3.27665759,  3.88831118,  3.23020961,  2.66780495,
                   2.64465832,  3.60061052,  6.01401723,  7.89548326,  8.32703461,
                   4.41891545,  2.42152952,  2.6098245 ,  1.7294729 ,  2.93136126,
                   1.68394869,  2.91366443,  4.51664704,  9.94660726, 11.32506517,
                   6.76098593,  5.39723631,  6.42688505,  4.10588407,  4.00985334,
                   4.12976916,  7.69937638,  6.4977388 ,  4.86823537,  4.54276589,
                   3.01302312,  3.30740392,  3.37291982,  2.82478807,  4.92758292,
                   4.49469951,  3.5431941 ,  4.51515325,  4.14233197,  4.63729334,
                   3.64555448,  3.66921355,  2.56344869,  2.88566611,  1.34577562,
                   1.34577562,  1.77014018,  4.08858701,  2.45948001,  3.07025213,
                   2.50961763,  2.99939208,  2.37004607,  3.10097109,  4.08021121,
                   4.63691772,  2.03887765,  2.34811391,  1.04269785,  1.04269785,
                   0.80471392,  0.80471392,  0.80471392,  0.77081487,  0.77081487,
                   0.77081487,  0.77081487,  1.03014649,  1.03014649,  1.86143078,
                   1.5793112 ,  2.66340155,  1.53636401,  1.69837212,  1.52557749,
                   1.51211135,  1.70648024,  1.72438164,  3.23553583,  2.7944787 ,
                   3.08500557,  3.88781694,  1.47355064,  2.80193376,  1.35404904,
                   1.3127965 ,  1.13950647,  1.20424311,  1.20424311,  1.08927672,
                   1.08927672,  0.87898571,  0.87898571,  0.87898571,  0.87898571,
                   0.87898571,  0.87898571,  0.87898571,  0.87898571,  0.87898571,
                   0.87898571,  0.87898571,  0.87898571,  0.87898571,  0.72964634,
                   0.72964634,  0.72964634,  0.72964634,  0.72964634,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.62748671,
                   0.62748671,  0.62748671,  0.62748671,  0.62748671,  0.84248774,
                   0.84248774,  0.84248774,  1.06774552,  1.44081773,  3.18823048,
                   1.02395912,  2.01333409,  3.47263825,  2.80606464,  3.38052228,
                   2.96385495,  3.0023371 ,  1.80680254,  2.15390124,  1.91558199,
                   2.16159335,  4.34825174,  7.35646385,  3.8553125 ,  4.21601191,
                   7.261817  ,  2.94324633,  2.99500021,  2.09640562,  1.96301932,
                   2.6940472 ,  1.64182455,  2.25968379,  1.7121704 ,  1.28678808,
                   1.79982589,  1.75975634,  1.53085263,  5.64012435,  2.38370669,
                   3.3699948 ,  1.39567957,  2.97868355,  3.62358452,  2.34408491,
                   2.12969017,  4.18694516,  1.72003964,  1.90244423,  1.69751186,
                   4.39806154,  2.77533503,  4.10661026,  3.746074  ,  4.30983161,
                   2.99226399,  6.88035776,  5.23941627,  2.87701026,  2.81654319,
                   3.51175694,  4.04919758,  3.45529549,  5.25623496,  5.09577817]])
      • created_at :
        2020-06-10T17:34:00.062215
        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
        • 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)
          <U16
          'Choate' ... 'Mt. Hermon'
          array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
                 'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype='<U16')
        • obs
          (chain, draw, school)
          float64
          16.12 1.001 13.59 ... 10.5 41.69
          array([[[ 16.12070379,   1.00077065,  13.5884531 , ...,  -3.32102967,
                    12.41474624,   5.3880134 ],
                  [  0.31286304,  10.87604623,   0.61156714, ..., -13.67640248,
                   -12.42821487,  22.54207407],
                  [  1.01770093,  19.85818733,  -4.68614833, ...,   7.65716318,
                    -0.69802287,  -4.49452911],
                  ...,
                  [ 12.48004901,  -1.78679224,  15.1745246 , ...,   7.98552349,
                    -3.17513437,  -1.08978072],
                  [ -7.19350203,   3.32676606,  18.59939682, ...,   6.55905051,
                     7.73231749, -12.15657743],
                  [ 26.06181938,  11.41170287,  -6.13354902, ...,   3.11098087,
                    10.11918758,  20.17803435]],
          
                 [[ -5.66449708,  17.73434902,  10.95330455, ...,  15.42521439,
                    -8.16076276,   9.16562713],
                  [ -8.94394888,  17.08611759, -14.87353811, ...,  13.25714385,
                     8.53916215,  25.7014456 ],
                  [ 19.34894266,  -3.46721825,   2.40651331, ...,  -7.76048036,
                    12.50213557, -32.98333085],
                  ...,
                  [ -2.28343942,  -8.00882316,  -1.31972725, ...,  -3.83927959,
                    27.4894464 ,  39.65246163],
                  [  3.63601625,  16.81393779,  35.16350247, ...,   5.2799238 ,
                    16.9409567 ,  12.78797208],
                  [  0.98247975,  27.4726395 ,   7.53983398, ..., -10.34939336,
                    10.49501115,  41.68533102]]])
      • created_at :
        2020-06-10T17:34:00.239971
        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
        • 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)
          <U16
          'Choate' ... 'Mt. Hermon'
          array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
                 'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype='<U16')
        • obs
          (chain, draw, school)
          float64
          -4.651 -3.318 ... -3.532 -3.809
          array([[[-4.65123378, -3.31803365, -3.71513164, ..., -3.33209802,
                   -4.07631976, -3.90733047],
                  [-4.82001547, -3.2598214 , -3.95921905, ..., -3.58326393,
                   -3.96039102, -3.86481386],
                  [-4.13731608, -3.24745981, -3.932011  , ..., -3.48166425,
                   -3.60144056, -3.85503224],
                  ...,
                  [-4.68063253, -3.24061135, -3.83288512, ..., -3.53883054,
                   -3.95525143, -3.85665762],
                  [-4.68063253, -3.24061135, -3.83288512, ..., -3.53883054,
                   -3.95525143, -3.85665762],
                  [-4.65686502, -3.22581717, -3.89596108, ..., -3.37835843,
                   -3.86504706, -3.85740931]],
          
                 [[-4.29898155, -3.24030745, -4.09864018, ..., -3.72878966,
                   -3.59158406, -3.81134889],
                  [-4.46562909, -3.30642214, -4.03403333, ..., -3.60634017,
                   -3.52743985, -3.81797455],
                  [-4.46562909, -3.30642214, -4.03403333, ..., -3.60634017,
                   -3.52743985, -3.81797455],
                  ...,
                  [-3.90987783, -3.23433871, -4.237528  , ..., -4.03261997,
                   -3.34076766, -3.88051681],
                  [-4.20441444, -3.24225028, -4.14548021, ..., -3.60112598,
                   -3.31553154, -3.81127625],
                  [-4.55287956, -3.24393767, -4.29187391, ..., -3.4485354 ,
                   -3.53151805, -3.80946587]]])
      • created_at :
        2020-06-10T17:34:00.237448
        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
          0 1 2 3 4 5 ... 495 496 497 498 499
          array([  0,   1,   2, ..., 497, 498, 499])
        • energy
          (chain, draw)
          float64
          54.11 55.93 56.07 ... 63.07 60.63
          array([[54.10601972, 55.93135612, 56.06957918, 55.33294634, 57.43933537,
                  59.07233325, 57.41813234, 59.74436832, 61.14341182, 60.7151683 ,
                  61.52439218, 60.54978452, 61.36221425, 60.56900019, 59.58650606,
                  59.50562608, 57.89948539, 55.61155433, 60.60662756, 62.05189116,
                  65.8980808 , 65.64044353, 72.10097787, 73.04449957, 67.82616163,
                  66.59270179, 63.1623821 , 62.37457397, 58.61424078, 68.22892012,
                  67.12878883, 66.20991738, 66.45800267, 64.14544431, 64.95653256,
                  67.51656333, 66.73294236, 66.83444633, 62.59751142, 67.81590809,
                  69.50951747, 69.43712505, 72.05196915, 68.93414382, 65.39200981,
                  65.68671149, 68.35139475, 66.4507085 , 69.250636  , 66.69110647,
                  65.10544319, 68.26589787, 72.07402017, 68.64816747, 60.99075786,
                  64.77252849, 64.22033057, 57.99900453, 56.46559097, 59.34801612,
                  59.50312128, 56.83820747, 60.92066642, 59.56365074, 58.57023478,
                  56.082646  , 58.98790289, 58.99157239, 61.71260227, 64.24304682,
                  64.55380337, 59.69909334, 60.26611304, 58.00049725, 59.83312984,
                  56.84846217, 60.02916461, 57.07925497, 58.97626349, 58.77919093,
                  54.95681999, 54.90718442, 65.76030564, 65.25573791, 65.67082321,
                  66.29131914, 64.93032832, 65.52818328, 66.55485846, 74.76445544,
                  68.0737226 , 67.97859506, 69.19217239, 64.72627295, 61.54529409,
                  56.48945637, 55.58834864, 61.01249983, 62.28958893, 66.5989684 ,
                  66.86429468, 64.10810704, 61.35159326, 63.45586947, 56.0620549 ,
                  54.36032021, 53.47257947, 60.34173746, 63.35189904, 62.14028342,
                  56.23034793, 53.52596934, 54.52112136, 54.13832771, 59.81806573,
                  55.17083226, 53.75113035, 58.92316936, 57.16635317, 61.27601319,
                  63.84307613, 63.44425436, 62.06467684, 63.47711012, 63.47588301,
                  61.46929645, 67.4437042 , 69.18878592, 68.45559514, 67.36887598,
                  63.40884125, 63.53038912, 62.02939071, 65.63861224, 68.22235368,
                  64.94645375, 55.75557397, 54.0450127 , 53.48238476, 51.54985226,
                  50.18766457, 48.85756009, 51.97660216, 47.32228709, 51.77660104,
                  53.0930875 , 46.6012184 , 47.90499327, 49.24975392, 51.36780241,
                  48.5813183 , 50.81037637, 48.92558874, 52.37554144, 57.11978216,
                  60.95167194, 62.65772985, 63.45560358, 60.98504135, 60.67911919,
                  61.5317335 , 63.17378632, 62.08554232, 61.57809938, 62.82500173,
                  61.37478009, 66.3078557 , 63.35831014, 64.9022637 , 64.76901128,
                  69.41440174, 69.38704195, 60.02769226, 60.62750495, 62.14914889,
                  60.63965897, 58.83558048, 55.41302767, 53.60311141, 53.8257481 ,
                  54.34645461, 55.87369572, 53.96962735, 54.49384491, 54.50993016,
                  54.43422357, 60.34752361, 59.06303724, 58.58756453, 57.31929054,
                  64.75296979, 68.74552087, 64.21555475, 62.49025073, 62.54264574,
                  65.77267494, 63.56636185, 70.46279215, 72.40638879, 72.94668148,
                  66.83747056, 67.07194183, 68.92777402, 67.56603533, 65.29801757,
                  63.12552762, 62.18858626, 64.53074004, 59.47838279, 64.12923403,
                  63.32403972, 64.09605252, 62.79529555, 69.2672079 , 77.54401582,
                  80.2982659 , 69.01530152, 62.98472869, 60.29743911, 58.57974915,
                  67.37778457, 67.37749577, 63.73610925, 59.71820764, 59.3628847 ,
                  61.22394581, 60.3522002 , 56.74099638, 58.73421852, 51.73590108,
                  51.70776294, 51.4989147 , 46.32772022, 46.18877034, 50.30087997,
                  53.13644562, 50.97989503, 52.34939691, 51.61819861, 49.8754385 ,
                  51.04828571, 47.42646789, 47.57567516, 47.15738502, 52.40590002,
                  55.05422805, 54.10464761, 50.34047244, 51.85475173, 51.96115223,
                  55.0713514 , 52.27938342, 52.56644345, 53.45380078, 54.54286479,
                  57.66023201, 58.81566635, 58.3466876 , 65.40265014, 59.3827241 ,
                  62.31599769, 65.23237765, 63.13343417, 63.03451414, 70.10100871,
                  68.94400215, 72.58169957, 68.40695964, 66.39347394, 69.98895933,
                  65.0492034 , 65.60198114, 64.06609554, 65.49535665, 57.86999135,
                  58.44554793, 58.52397693, 64.24340097, 59.40212154, 55.99945362,
                  57.30856274, 63.00779274, 62.20179632, 64.38798482, 63.43418645,
                  63.07314845, 64.52374228, 65.04943275, 67.7777635 , 64.83709177,
                  61.09276616, 53.4143787 , 55.12341918, 49.51919281, 47.15804344,
                  51.11525597, 47.2995792 , 51.2100775 , 55.05619063, 51.64273438,
                  51.60193566, 53.90630626, 53.37859907, 51.0531472 , 55.8125039 ,
                  60.55508193, 58.45580218, 56.61282754, 59.14732549, 58.46471393,
                  56.47607621, 58.93691097, 60.37981461, 63.20065984, 64.33952011,
                  60.56063989, 59.56529761, 59.05735166, 57.16836299, 57.64805983,
                  60.75841121, 62.17599997, 66.94291735, 67.43151337, 70.51928215,
                  69.62293541, 70.28592791, 73.49247495, 71.25395936, 81.53398362,
                  77.28702655, 66.92878818, 63.54807272, 63.87554542, 67.9316875 ,
                  59.55586943, 68.4689987 , 65.81188095, 67.58851407, 68.6245911 ,
                  68.41912778, 65.80920182, 69.02568047, 70.64528984, 69.16773546,
                  63.40629269, 65.1410899 , 63.00736498, 61.78761687, 66.46462664,
                  63.2910019 , 65.57525585, 69.39381403, 72.43189069, 72.97748229,
                  69.53065595, 62.32524486, 60.75009471, 65.41650235, 58.82340072,
                  57.62234976, 56.23104945, 52.05068993, 57.77585883, 59.08139477,
                  57.81904431, 53.7280486 , 53.08016937, 52.60640982, 54.17433158,
                  54.74670936, 59.56887897, 61.43993805, 65.45781501, 61.81370826,
                  63.6799869 , 62.29196608, 65.25805627, 69.85652606, 66.09235923,
                  63.4692679 , 65.22944575, 66.03535827, 75.23938921, 73.83506969,
                  68.72891395, 70.88868616, 70.82175873, 69.5697375 , 65.1836767 ,
                  59.61316137, 54.54615491, 58.37597463, 57.52522281, 57.07714297,
                  59.41840899, 60.40184249, 53.6413567 , 53.04231423, 57.75461201,
                  56.72590066, 56.67385048, 55.68381775, 52.73433905, 56.44556211,
                  56.4077514 , 57.28035558, 53.72090604, 58.87717811, 61.80988539,
                  59.1003976 , 58.18190188, 59.15584218, 56.88896863, 57.45712783,
                  58.79597887, 59.48728147, 65.14175357, 67.05126203, 72.98578478,
                  69.47359651, 68.3128967 , 65.48785988, 66.67854362, 71.92791313,
                  70.32314241, 70.93850983, 72.19582617, 65.58886169, 66.54167174,
                  66.77739505, 67.17919099, 65.97313583, 66.12847021, 66.37077162,
                  65.39077702, 66.02386045, 68.92655272, 67.23746742, 63.47133117,
                  62.90333626, 62.84304656, 64.36057003, 72.59633793, 69.72091488,
                  69.17577819, 67.86658525, 61.14516516, 62.80944752, 63.39108239,
                  61.85910542, 61.49439461, 56.83414815, 54.29448161, 57.06753066,
                  53.81617812, 60.54420739, 64.02815631, 62.20980492, 61.72451974,
                  62.61419121, 62.49293563, 64.59334416, 61.83543094, 67.74919359,
                  63.69267265, 68.05979035, 66.60549507, 66.41192104, 68.74720436,
                  69.48224055, 71.17564153, 66.59538684, 66.19871719, 60.93792004,
                  60.87871881, 64.00857709, 63.45486055, 64.7533642 , 67.64134898,
                  71.23802865, 65.27106083, 63.14943176, 68.54167124, 68.16367718,
                  66.52899007, 63.28037528, 59.26195905, 65.96123023, 67.20003219,
                  66.85327017, 62.7872037 , 61.15546027, 62.88457413, 62.24576625,
                  58.89839906, 56.11340163, 52.37056991, 56.02808218, 51.3536903 ],
                 [53.60244548, 52.69386493, 54.44602084, 53.75236244, 52.35215801,
                  49.32314787, 49.58063386, 59.07849524, 63.63249153, 56.7319414 ,
                  61.7355117 , 61.85442926, 61.19520594, 62.53248808, 67.98347609,
                  65.98401171, 66.2309188 , 62.95105882, 61.98967592, 73.7081029 ,
                  70.85678495, 67.17534704, 67.10515254, 63.97530304, 62.71759842,
                  62.06703675, 69.628179  , 68.95994287, 65.81240029, 60.00739701,
                  59.12269304, 61.23871578, 61.99409798, 62.06859449, 61.30373254,
                  58.57243878, 62.25424113, 56.14413632, 59.93667047, 58.71816755,
                  55.93221947, 54.03138541, 53.73444051, 53.76537658, 55.49506147,
                  57.97763145, 57.97804552, 60.73505002, 65.22473727, 64.33972018,
                  60.18207915, 59.89928505, 57.97880735, 64.66007689, 65.80358903,
                  70.92688126, 65.92775749, 65.00798582, 61.80155031, 61.84010643,
                  61.02408525, 61.57800602, 68.29254652, 67.29366737, 67.73589223,
                  64.77047529, 61.56603755, 58.55503939, 55.32132955, 57.16421665,
                  55.5711269 , 57.37014229, 59.17605274, 67.53378929, 64.87552913,
                  65.85111842, 72.05159791, 68.26888059, 67.69275939, 75.5699396 ,
                  69.60763391, 72.17720205, 70.80473007, 66.64958448, 67.20071524,
                  68.47473224, 68.64765914, 72.82855058, 73.95378175, 72.84928973,
                  72.84266759, 73.80330984, 68.64266644, 59.27433228, 57.84598801,
                  56.07467704, 57.13500866, 54.85460647, 56.02934415, 58.17856125,
                  57.74377082, 57.99227912, 60.23866246, 61.53175894, 68.01831885,
                  68.72735029, 65.04507207, 65.41968704, 68.16321724, 62.64571234,
                  62.43054438, 59.98861128, 61.15481692, 62.7242483 , 60.24558531,
                  58.11589587, 66.49193714, 58.63776453, 64.09510091, 59.92864502,
                  57.16172046, 56.60649595, 58.13968405, 57.3753964 , 58.15799169,
                  60.83792045, 62.29265995, 58.3021099 , 59.79733266, 61.71560823,
                  58.25353651, 59.22641181, 61.92456386, 61.06434309, 65.17219157,
                  67.07149993, 59.64610708, 60.37267406, 61.27449751, 55.73856904,
                  53.90898524, 57.99588252, 61.41298203, 63.69683754, 65.91247566,
                  63.66712525, 65.32871947, 63.69239101, 73.51460897, 68.65636017,
                  73.49083406, 72.12184762, 66.57885957, 65.11903592, 62.89009805,
                  60.10017418, 55.75733925, 56.98647405, 61.09134149, 59.51205313,
                  59.00974101, 62.20060436, 64.71632587, 63.72456551, 59.6069249 ,
                  60.23073323, 64.34181123, 58.53885833, 55.90696959, 66.40857614,
                  70.07465822, 61.39868071, 63.19341297, 62.74412198, 64.15468006,
                  71.92735942, 74.14983813, 74.12862851, 67.76347352, 65.29863877,
                  65.57332131, 65.62659245, 64.82969051, 66.07240255, 64.70862794,
                  64.41535676, 66.05266669, 67.94336575, 65.38734235, 64.84508242,
                  63.66121546, 62.96759965, 62.77539639, 58.99623244, 59.49273167,
                  52.52354063, 54.6607846 , 49.43338266, 52.41974133, 52.95769922,
                  61.69145629, 64.42912534, 61.94745804, 62.23649514, 67.62535896,
                  67.37877203, 66.01274553, 64.01757759, 58.80340238, 62.03810109,
                  63.35527724, 69.76194838, 68.10245826, 68.04552492, 64.21840458,
                  64.33290518, 67.27655669, 66.3713469 , 60.51734284, 62.88616166,
                  62.94277232, 64.12384569, 62.84366182, 63.29697183, 59.40593025,
                  60.83477564, 66.99727531, 72.1593534 , 73.72928373, 62.22556448,
                  57.03300449, 58.85981984, 61.14298194, 62.43610698, 64.38508799,
                  67.76257956, 67.79498144, 67.41364534, 67.54706612, 62.62947301,
                  59.71996079, 60.93108646, 56.7865272 , 58.64598487, 52.56063956,
                  54.22003327, 55.01444707, 56.7049828 , 59.23566292, 63.40569895,
                  66.78481514, 64.34452282, 62.84669753, 64.83183415, 61.55412974,
                  58.54992206, 55.44222381, 53.63911963, 56.46056661, 58.14077911,
                  55.86199611, 57.62349341, 58.42708705, 57.29943901, 54.01071821,
                  56.10170348, 54.72271618, 61.19420951, 54.10362547, 54.16863958,
                  59.60536296, 63.48124574, 58.22722364, 58.27765496, 57.27205882,
                  55.68972879, 64.97996995, 62.50022593, 65.60620959, 64.12540485,
                  62.41568365, 60.18061354, 65.13470809, 58.05569341, 59.48033937,
                  56.30606088, 61.63911117, 63.09263898, 67.19901662, 67.87459557,
                  66.07676332, 64.89155346, 63.37177986, 62.09316402, 61.88759968,
                  58.7062763 , 60.1085988 , 61.94359896, 65.35902755, 64.23400904,
                  64.46559548, 60.9470359 , 63.31525258, 63.2422965 , 61.29543503,
                  59.33070188, 61.03346519, 58.57095782, 59.70237867, 62.44783064,
                  61.60947356, 63.1706247 , 60.21548279, 59.90134771, 54.0485363 ,
                  55.14613596, 57.79197049, 55.78038696, 55.21524072, 55.6709634 ,
                  58.90081847, 59.5807061 , 60.46488242, 60.02755387, 60.08491252,
                  60.67368076, 61.28101165, 56.43155706, 56.18548809, 58.46799956,
                  56.20708753, 50.65697662, 55.13999495, 51.22520453, 53.7256044 ,
                  51.35089862, 55.4405572 , 51.19459286, 49.6482886 , 50.81612651,
                  51.37536988, 55.08973124, 54.83025627, 52.84083862, 52.99210807,
                  51.38413862, 51.41213848, 63.92944477, 61.25401367, 56.53271071,
                  60.45375526, 58.21645597, 58.96260301, 55.75966373, 53.07683131,
                  52.31842166, 55.99994602, 52.56370159, 54.80220901, 51.50756231,
                  52.60058165, 50.42554838, 49.05310549, 50.07197869, 52.65312348,
                  49.24796023, 48.24791924, 51.75575504, 49.20175309, 49.18472907,
                  51.57103738, 51.45009932, 47.99143565, 48.62475201, 47.68566231,
                  46.9351184 , 49.87228692, 49.58910092, 46.02329267, 46.24468298,
                  45.73329771, 49.71074505, 45.52933137, 46.69956299, 45.59818208,
                  52.72025749, 48.20671223, 48.12730909, 48.34757922, 48.79037513,
                  46.59685804, 47.72113315, 44.57566664, 49.10271775, 45.54127919,
                  47.94160497, 49.81016604, 51.75385238, 49.89643918, 47.0728521 ,
                  45.96138862, 52.39496693, 47.41221204, 46.39057563, 46.64714747,
                  51.62987482, 45.76652167, 47.96629965, 44.32672795, 46.04865811,
                  45.70867166, 46.05054711, 46.56539042, 46.56833445, 45.60902209,
                  52.0347991 , 49.77467629, 47.01444296, 44.38546413, 47.56712426,
                  51.11780153, 47.04331029, 46.84185003, 49.28623687, 50.24205743,
                  46.38140425, 48.94254973, 44.57800771, 44.0545092 , 48.55961343,
                  45.21743439, 52.39477459, 46.05959038, 49.4004143 , 48.84947639,
                  48.61981029, 46.13661078, 54.58317632, 52.8695073 , 48.03907558,
                  53.03332862, 47.86037014, 53.03023093, 51.86923605, 56.4412707 ,
                  54.07619099, 51.54000012, 62.33058655, 60.65361866, 63.6944786 ,
                  59.32092297, 59.4021599 , 56.18655547, 55.83749394, 60.04084771,
                  58.01303146, 59.94967534, 62.81270834, 64.57007364, 59.91083213,
                  66.02914727, 67.41535085, 62.09908459, 61.70327093, 54.30156607,
                  60.08155721, 58.2182457 , 56.85473782, 53.94345267, 56.40689502,
                  51.80366378, 51.32023053, 49.95956705, 58.27866826, 58.95188507,
                  60.64881579, 61.25014988, 56.30228326, 58.90363424, 59.3794847 ,
                  57.50474111, 59.46426876, 59.41943095, 57.70590674, 52.00731936,
                  59.13225558, 59.4024256 , 62.26998709, 62.98073981, 60.24202472,
                  56.49984444, 59.49194813, 63.65820625, 62.88547029, 61.13551938,
                  58.73484369, 62.27303891, 66.52603402, 63.06981985, 60.62919504]])
        • max_energy_error
          (chain, draw)
          float64
          -0.2159 1.599 ... -0.4515 -0.5108
          array([[-2.15922042e-01,  1.59851393e+00,  3.45938191e-01,
                   1.49101606e-01,  6.66302062e-01, -1.72598192e+00,
                   1.12704939e-01, -2.00394457e-01, -3.16009354e-01,
                  -9.48832164e-01,  5.29485426e-02, -4.59256185e-01,
                  -1.98361439e-01,  2.69894087e-01, -1.41242448e-01,
                  -1.00846863e-01, -5.02984547e-01,  1.03067685e+00,
                   3.24636488e+00, -6.19085987e-01, -5.83079659e-01,
                   3.53893700e-01,  2.39631108e-01,  1.21761877e-01,
                  -2.63124349e-01, -3.39035967e-01, -4.51785177e-01,
                  -2.88341458e-01, -5.59996662e-01,  5.58103361e-01,
                   8.45622746e-02,  4.89708136e-01, -2.63709450e-01,
                  -1.37949190e-01, -2.21305227e-01,  1.27328285e-01,
                   7.68702041e-01, -1.86826020e-01,  2.32594754e-01,
                   2.14098750e-01,  2.71504934e-01,  5.79404463e-02,
                   9.50991170e-02, -1.17361820e-01, -6.12747036e-02,
                  -2.19940369e-02, -7.47584158e-02,  4.18356792e-02,
                   2.23495920e-02, -4.14647333e-01,  4.12499387e-01,
                   3.79905927e+00,  1.01674164e+00,  5.71866852e-01,
                  -2.35100086e-01,  1.93536806e-01, -1.10292728e-01,
                   7.50123383e-02, -6.45553131e-02, -6.27479061e-01,
                  -1.01783599e-01, -1.89693967e-01,  2.61339435e+00,
                   2.23838574e-01,  6.79816102e-01, -1.52673505e-01,
                  -2.20089584e-01,  1.35764007e-01, -5.20947117e-01,
                  -1.30486283e-01,  4.87051405e-01, -3.23180727e-01,
                   3.71142453e-01,  7.44223952e-01,  6.89249248e-01,
                   6.08444859e-01,  3.80846446e-01, -3.63354087e-01,
                   3.01487280e-01,  3.02083854e-01,  5.48682028e+02,
                  -1.80253075e-01,  9.55729442e-01, -4.75034328e-01,
                   3.50122724e-02,  7.12301112e-02, -1.37035626e-01,
                  -3.46853386e-01, -1.37533733e-01,  5.03724526e-01,
                   2.10604975e-01,  4.94969761e-01, -2.62129960e-01,
                  -1.46056259e-01, -2.32308101e+00, -6.07169979e-01,
                  -1.52387231e-01,  6.79397385e-01,  4.47458423e-01,
                  -3.56666172e-01, -1.27263503e-01, -1.01199985e-01,
                  -2.22863308e-01, -8.23553458e-01,  8.68747381e-01,
                   1.88440942e-01, -2.82893479e-01,  3.77220490e-01,
                   3.54180500e+00,  2.57822560e+00, -2.77263378e+00,
                  -9.30270898e-01,  2.11063260e+00,  2.62589045e+00,
                   1.30598466e+02,  1.15512078e+01,  6.96795206e+00,
                   4.08172677e-01, -4.48535275e-01,  4.46117606e-01,
                   1.92472624e-01, -1.21867366e-01, -7.75596000e-02,
                  -2.47111320e-01, -7.85851230e-02, -1.36183646e-01,
                   8.65380021e-02,  2.33637920e-01, -4.27178026e-01,
                   3.85826251e-01, -3.06886910e-01, -7.48087621e-02,
                  -4.61733537e-01,  1.78833226e-01, -2.60747146e-01,
                  -7.91908447e-01, -7.69884347e-01,  9.85962921e-01,
                  -9.91972474e-01,  3.16243722e+00,  1.97269716e+02,
                   6.63084424e+02,  1.36983156e+02,  1.22738075e+03,
                   8.02371811e+01,  1.73670003e+02, -4.95519595e-01,
                   3.30987036e+03,  2.69983204e+00,  2.32023383e+01,
                   4.75381860e+01,  3.52031919e+01,  1.24408199e+03,
                   4.93082548e+00,  2.87569969e+00,  3.45188144e+00,
                  -3.85523877e-01,  1.06735845e+00, -6.18705206e-01,
                  -3.29389576e-01, -3.84729247e-01, -2.29067364e-01,
                  -7.07171270e-02,  1.19231491e-01,  2.95848128e-01,
                  -1.49421848e-01,  9.32182014e-01,  3.97107459e-02,
                   3.00097364e-01, -3.17860522e-01, -4.11842298e-01,
                  -6.08347920e-01, -3.07958099e-01, -1.43366613e-01,
                  -3.65616198e-01, -2.78185116e-01,  2.18515698e+01,
                   1.11211754e+01,  1.16681756e+00, -9.95737545e-01,
                   1.82139078e+03,  1.31865511e+00,  3.91280699e+01,
                   1.46137724e+00,  4.70093267e-01, -6.10677225e-01,
                   4.91825084e+00, -2.36475861e-01,  3.30231074e-01,
                   5.15932348e-01,  6.27231997e-01, -9.52884215e-02,
                  -2.09591482e-01,  4.29408156e+00, -5.14656805e-01,
                  -1.10251714e+00,  9.45545953e-01,  4.66791643e-01,
                   3.89485423e-01, -2.07183356e-01, -3.65831636e-01,
                   2.39752659e-01, -1.40062489e-01, -3.17099572e-01,
                   1.50951578e-01, -1.86787262e-01, -1.60043642e-01,
                   4.77797462e-01, -6.09913080e-01, -3.14939159e-01,
                  -4.07645785e-01,  3.05033698e-01, -3.72488005e-01,
                  -4.21153375e-01,  2.20180449e-01, -2.19551585e-01,
                   5.37056224e-01, -1.90744714e-01, -1.27354638e-01,
                   9.64904720e-02,  2.95928103e+00, -3.97397987e-01,
                  -3.68958429e-01,  3.75495302e-01,  6.28909286e-01,
                   2.09189975e-01, -2.04267761e-01, -1.73494208e+00,
                   1.47723522e+00,  7.51621341e+01,  5.12907638e+01,
                   1.32452618e+02, -7.38665984e-01,  4.77493668e+02,
                   1.41230903e+02,  7.20686184e-01,  2.61401967e-01,
                   8.41223824e+01,  1.58980236e+00,  4.59902271e+01,
                   1.66482528e+00,  5.63897906e+03,  9.86954916e+00,
                   1.39186308e+01,  7.80354466e+01,  1.06976716e+03,
                   1.25646140e+02,  2.04620485e+02,  6.35405903e-01,
                   1.81069003e+02,  3.21281380e+01,  8.61225841e+00,
                   3.41925093e+02, -2.43590064e-01,  1.10036418e+00,
                   5.03329666e-01,  2.78030000e-01, -9.88509293e-02,
                   3.59636401e-01, -2.11677785e-01,  6.20980873e-01,
                   6.90337052e-01,  2.77959078e-01, -3.22558527e-01,
                   2.84217994e-01, -1.55702300e-01, -1.08693831e-01,
                  -1.51459294e-01, -1.63555792e-01, -4.58076028e-01,
                  -3.05881764e-01, -5.59415499e-01,  1.18597677e-01,
                  -1.51215968e+00,  4.79342776e-01, -3.74547454e-01,
                  -4.28099602e-01, -3.26208957e-01, -2.57816607e-01,
                  -1.80147632e-01,  1.92005312e+02,  3.60333715e-01,
                  -8.43951154e-02,  3.06537175e-01, -2.00620480e-01,
                  -3.46021065e-01, -2.98262855e-01,  9.32081589e-02,
                  -3.22852413e-01,  2.72965203e-01, -7.49017799e-01,
                  -3.07951607e-01,  4.88887770e+00,  1.97940716e+00,
                   3.07998232e+00,  1.00555763e+02,  2.60881099e+02,
                   5.66972739e+01,  2.75102428e+01,  2.14717690e+02,
                   2.53963720e+03,  1.19887472e+02,  2.18353602e+01,
                   1.55394394e+01,  1.35215353e+02,  6.21319387e-01,
                  -6.69678313e-02,  1.89084843e-01,  2.41621811e-01,
                  -6.40051198e-01, -1.02393995e+00,  2.28690872e+00,
                  -4.14405714e-01,  2.65891904e-01, -6.72107659e-01,
                  -2.96286757e-01, -8.15053209e-01,  3.26683125e-01,
                   2.10658514e+00,  1.44849197e-01,  3.41176417e-01,
                   3.14755121e-01,  3.45383333e-01, -1.43796072e-01,
                   6.20623041e-02, -8.31338415e-01, -9.19758336e-02,
                  -8.56204619e-02, -1.92713055e-01,  1.67501680e+00,
                  -9.51299439e-01,  2.04222920e-01, -1.51587221e-01,
                  -2.86415317e-01,  1.76001976e+00, -2.00330472e-01,
                   2.88616150e-01, -1.11352669e-01, -1.06644772e-01,
                  -3.90763547e-01, -1.99974717e-01, -2.19659405e-01,
                   8.90989463e-01, -2.41506797e-01, -2.35950417e-01,
                  -2.58898448e-01, -5.40428209e-01,  5.25791438e-01,
                  -1.84546622e-01,  1.81253680e-01,  6.53181702e-01,
                  -5.21721215e-01, -3.86453290e-01,  1.21059052e+00,
                  -4.10453940e-01,  7.81388667e-01, -2.37459240e-01,
                  -3.92563277e-01,  4.89160930e-01, -8.57304040e-01,
                   3.22276802e+01,  1.23930761e+00,  3.83900895e+00,
                   1.10581511e+00,  2.31663645e+00,  5.00134127e-01,
                   6.33298812e-01,  1.70824626e+03,  5.29668274e+00,
                   2.44921752e+00, -2.55004556e-01,  2.83130121e-01,
                   6.63295101e-01,  4.66279570e-01, -9.79329341e-02,
                   1.58312789e-01, -2.51546323e-01,  5.64101474e-02,
                  -5.93909791e-02, -1.89051715e-01,  1.18568390e-01,
                   3.20938754e-01, -2.80143006e-01,  2.55210169e-01,
                   3.47426836e-01,  7.63459587e-02, -6.11688117e-02,
                  -5.55281232e-02,  1.88530157e-01, -4.10742153e-01,
                  -2.07025111e-01,  1.86848599e-01,  7.41928855e-01,
                  -7.23799915e-01, -2.40243923e-01, -2.93007023e-01,
                  -5.79063729e-01,  1.74649291e+00,  4.10620482e-01,
                   2.65384059e+00,  1.60023034e-01,  9.37904880e+00,
                  -2.05205314e-01, -1.71723184e+00,  3.09027148e+00,
                   3.70994921e+00,  6.49912567e+01,  1.45993585e+01,
                   1.64372413e+00, -1.03136855e+00, -2.04426584e-01,
                  -3.54213304e-01, -2.03980763e-01, -3.36301561e-01,
                   1.03419257e+00,  3.08387428e-01, -6.23033351e-01,
                   1.70472323e-01, -6.13504944e-01,  1.85482788e-01,
                  -5.93042263e-01, -3.01327418e-01, -2.08697621e-01,
                   9.32953593e-01,  8.23823106e-02,  4.63452449e-02,
                   4.05173987e-02,  2.37695013e-01, -2.65350030e-01,
                   4.67890569e-01, -7.38705861e-02,  2.96614475e-01,
                  -2.48210902e-01,  1.85879022e-01, -1.37576749e-01,
                   5.17895630e-01,  2.07809683e-01, -4.63220522e-01,
                   3.76257418e-01,  1.67598439e-01,  2.87942127e-02,
                  -1.76475462e-01, -1.54681771e-01, -8.90181608e-02,
                  -8.41236474e-02, -1.53567957e-01, -1.43814097e-01,
                  -4.30972667e-01, -4.30075406e-01, -1.51133197e-01,
                  -9.58065183e-02, -4.42529118e-01, -5.55840346e-01,
                   1.99354930e+00,  1.88315211e+00, -2.62253325e+00,
                   1.89002397e+00, -2.63519513e-01, -4.06767618e-02,
                  -2.87430150e-02,  8.12267578e-02,  5.21495502e-01,
                   7.78623481e-01,  2.82236783e-01,  8.93584705e-01,
                   9.70442983e-02,  3.35710421e-01, -2.96074612e-01,
                  -1.78928226e-02,  2.89458817e-01, -3.26735303e-01,
                  -1.64817790e-01,  1.05354759e-01, -4.56366851e-01,
                   3.62683856e-01, -3.00254498e-01,  2.76500387e-01,
                  -2.57542516e-01, -1.66610389e-01,  5.12700971e-01,
                  -3.75878082e-01, -1.23418222e-01, -3.25394683e-01,
                  -2.85193591e-01, -5.35925352e-01, -7.83295346e-02,
                  -1.24419209e-01, -7.95992486e-01, -3.23350145e-01,
                   2.57317417e-01, -2.43837819e-01, -1.80618914e-01,
                   5.43407325e-01, -4.75768057e-01,  1.86096491e+00,
                   3.00420772e-01,  5.35262001e+01, -1.27889607e+00,
                   5.95335768e+01,  5.73677789e+00],
                 [ 3.00300272e-01,  7.11432161e+00,  5.05496442e+01,
                   1.19203159e+02,  1.62655644e+02, -6.98527960e-01,
                   4.04149342e+03,  2.76559442e+00,  8.42397179e+00,
                  -4.27086304e-01,  1.49966671e+00, -1.88819316e-01,
                   1.81336178e+00, -1.48354988e-01, -1.12452980e-01,
                   7.05268482e-02, -3.49979073e-01, -4.78196331e-01,
                   1.89891636e-01,  2.63677169e-01, -4.80490177e-02,
                  -5.01409326e-02,  3.78750522e-01, -1.42681116e-01,
                  -2.28536138e-02, -1.20084147e-01,  5.36035669e-01,
                  -2.52745349e-01, -2.28735394e-01,  1.17650377e+02,
                  -3.96986865e-01, -1.98869804e-01,  9.94955835e-01,
                   2.04628426e-01, -1.74962931e-01,  7.14793714e-01,
                   3.82844502e-01,  1.10834308e+00,  1.79578742e-01,
                   1.53278459e+00, -7.02388712e-01,  4.02193461e-01,
                  -3.57069869e-01,  1.28016962e-01,  4.07908363e+00,
                   4.22346025e-01, -1.92318006e-01,  1.41209017e+00,
                   2.03314732e-01, -1.61239386e-01, -3.07224819e-01,
                  -1.43263739e-01, -8.14831593e-01,  1.52634648e-01,
                  -1.78322178e-01, -2.16347647e-01, -4.79893103e-01,
                  -1.49763580e+00, -2.89315939e-01, -3.29202730e-01,
                   1.71063602e-01, -1.32616962e-01,  4.13554455e-01,
                  -3.03856839e-01, -5.11164704e-02, -1.48839338e-01,
                  -3.99097482e-01,  4.11033270e-01,  4.50300076e-01,
                   6.83490393e-01, -8.73907058e-02,  2.33249951e-01,
                  -6.87472058e-01,  1.65453985e-01, -9.91214868e-02,
                   3.20685059e-01, -2.04990960e-01, -3.63082175e-01,
                   3.25009724e-01, -2.70649788e-01, -2.19104789e-01,
                  -3.29411593e-02, -1.41368817e-01,  7.51583456e-02,
                  -5.21123846e-02, -1.49086731e-01,  1.83149428e-01,
                  -3.34452187e-01,  2.56186079e-01, -1.13905584e-01,
                  -3.12227227e-01, -6.42441449e-01, -1.23843840e+00,
                  -1.96921722e-01,  2.47851995e-01, -2.18804235e-01,
                  -9.11038049e-01, -4.08059673e-02,  1.25591830e-01,
                  -7.95458593e-02, -1.44174187e-01, -5.12687299e-01,
                   9.26496887e-01, -3.10721967e-01,  4.35672314e-01,
                  -3.02110032e-01, -1.64302195e-01, -6.53973895e-01,
                   5.82854925e-01, -1.69874779e-01, -1.39755373e-01,
                   1.65456901e-01, -4.28968041e-01, -2.61699915e-01,
                  -4.77689499e-01,  9.10978258e-02,  2.35905535e-01,
                   5.43072673e+00,  9.29193344e+01,  2.88183482e+00,
                   4.07128592e-02,  3.06294942e-01,  8.83137290e-01,
                  -3.85834208e-01, -2.07505220e-01, -3.56392635e-01,
                   4.40744105e-01, -2.68064946e-01,  1.03402983e+00,
                  -1.24574773e+00, -4.57001986e+00, -2.68244557e-01,
                   1.39046501e-01, -1.38067208e-01,  1.50252653e-01,
                  -9.78763531e-02,  1.30524126e-01,  1.70774457e-01,
                  -1.24668201e+00,  9.95656899e+00,  1.18702381e+02,
                  -8.45360357e-01,  3.64428035e-01,  9.62962465e-01,
                  -6.86973399e-01, -5.29671916e-01, -3.51465076e-01,
                   2.36127955e+00, -3.12824408e-01,  3.69727536e-01,
                  -3.01595460e-01, -4.19632618e-02, -1.33130730e+00,
                   2.92707225e-01, -6.03437404e-01, -1.16624143e-01,
                  -4.19839101e-01,  6.83689747e+00, -2.02604014e-01,
                  -3.03362087e-01,  1.83406338e-01,  1.41306146e-01,
                  -7.52885811e-02, -4.23237965e-01,  2.23052536e+00,
                  -2.83451876e-01, -4.13313155e-01,  9.88704848e-01,
                  -7.75025123e-01,  9.54275355e-01, -1.34125338e-01,
                  -1.77518830e-01, -1.79001681e-01, -3.79549787e-01,
                   9.18926124e-02, -6.10879624e-02,  3.47721082e-01,
                   4.88907906e-01, -6.32869094e-01,  2.79324826e-01,
                  -4.54784465e-01, -8.93597108e-02, -1.64697993e-01,
                  -1.98512944e-01, -9.33562150e-02, -1.41948567e-01,
                   6.25537261e-02,  8.22924274e-02, -7.79331225e-02,
                  -1.17060885e-01,  1.58064112e-02, -1.15469115e-01,
                  -6.86668735e-01, -9.89323363e-02,  4.11220935e-01,
                  -7.76478750e-01,  9.54951759e+01,  1.17064142e+02,
                   2.35254144e+01,  2.98043780e+02,  2.68957702e+00,
                   4.20294050e-02, -5.01589211e-01,  8.89880983e-01,
                  -7.57280482e-02,  9.73872873e-02, -3.95493967e-01,
                  -1.13105532e-01,  2.58760704e+00, -6.08285110e-02,
                   1.73650426e-01,  2.06287690e-01, -5.91055584e-02,
                   1.22365351e-01,  6.79916216e-02, -1.53922283e-01,
                   3.07007776e-01, -6.41036583e-01,  6.96509564e-02,
                  -3.59589982e-01,  7.06060476e-02, -2.18518960e-01,
                  -8.85809574e-02,  3.71234225e-01, -1.93846586e-01,
                   1.24341834e+00,  2.87021880e-01, -1.11155419e-01,
                   4.63711353e-01, -3.09420741e-01, -4.18031547e-01,
                  -4.95419020e-01,  2.47071542e-01,  1.58009422e-01,
                   1.26178664e-01, -1.78838698e-01,  9.91700975e-02,
                  -7.70774943e-02, -1.12219600e-01,  1.89641137e-01,
                  -1.34408788e+00,  3.36659934e+01,  8.96311494e+00,
                   1.46727009e+00,  4.60187154e-01, -1.89280410e-01,
                   2.12092622e-01,  4.76227207e-01,  5.88963484e-01,
                  -2.14407613e-01,  9.02930112e-01,  7.56696787e-01,
                  -2.48283124e-01, -3.59253267e-01, -1.11486676e+00,
                  -1.20388240e+00,  5.70638647e+00,  1.56561377e-01,
                   5.87319831e-01,  1.37351994e+00, -3.28260378e-01,
                   6.01272105e+01,  3.36407157e+00,  7.06031737e-01,
                   2.71894430e-01, -5.66135528e-01,  7.58358685e-01,
                   3.59184114e+00,  2.66072910e+00,  5.56748081e-01,
                  -1.15245210e+00,  4.96296008e-01, -1.64176669e-01,
                  -4.88912533e-01,  5.24135049e-02, -2.00168055e-01,
                   2.90716288e+00,  3.25101057e-01, -3.68067307e-01,
                   2.83516690e+00,  4.54045078e-02, -5.14124585e-01,
                  -8.28897736e-01,  2.21092967e-01, -1.43225784e+00,
                   2.85553060e+00,  1.07059928e+00,  2.22472765e-01,
                  -2.69924885e-01, -1.64919967e-01, -2.77987470e-01,
                  -1.61334187e-01,  1.57908366e-01, -3.32341597e-01,
                   1.56228915e-01, -1.30121260e-01, -5.38510415e-01,
                  -7.63610174e-02, -2.70356488e-01,  1.41117824e-01,
                  -9.54720997e-01, -3.42227575e-01,  3.06353865e-01,
                  -4.17459801e-01,  2.23485038e-01, -1.96507014e+00,
                  -1.36515265e-01, -5.84637989e-02, -7.84971934e-01,
                  -1.69196984e-01,  1.56022558e-01, -9.67812465e-02,
                  -4.04384206e-01,  6.88864204e-01,  2.42267634e+01,
                   7.20040367e+00,  2.88478881e-01,  3.43207189e+00,
                  -3.91076835e-02, -3.47646968e-01,  7.98269152e-01,
                   1.61915168e-01,  2.95862020e-01, -2.93946891e-01,
                  -7.28555656e-01, -6.85879598e-01, -6.49119560e-01,
                   1.20382546e+01, -2.42842604e+00,  3.40891039e+02,
                   4.23577532e+01,  6.58725253e+00,  2.49861358e+01,
                   6.58706266e+00,  7.74671952e+01,  1.40412913e+03,
                   1.00134303e+03,  4.96362135e+00,  1.64401619e+02,
                   7.41151579e-01,  1.73585605e+00,  3.74205040e+00,
                   1.48162418e+00,  1.51033247e+00,  5.12098367e+00,
                   5.30642798e+01, -1.32887115e-01,  2.83074320e+00,
                   1.97088016e+00, -3.30474008e+00, -6.42578344e-01,
                   1.16362217e+02,  1.02821582e+00,  1.14122429e+00,
                   1.26364051e+00,  8.40234931e-01,  4.29255499e+00,
                  -1.05917655e+00,  2.65640497e+01,  5.88380133e+01,
                   4.66312751e+00, -1.14124013e+00,  1.14037408e+01,
                   4.05557981e+02,  8.60227539e+00,  4.05752779e+02,
                   1.81495055e+02,  5.56321371e+01,  3.11665841e+02,
                   1.25260080e+03,  2.43715582e+02,  1.77499088e+03,
                   8.40781883e+01,  1.55373461e+01,  2.54295529e+03,
                   3.61263439e+01,  9.44074575e+01,  1.36024253e+01,
                   2.47711898e+01,  3.76886967e+03,  6.95653349e+01,
                   9.25919922e+01,  1.54105634e+02,  7.31975394e+01,
                   1.47058099e+02,  6.32600492e+02,  8.70406660e+01,
                   6.88907656e+01,  4.56324636e+01,  7.28355455e+02,
                   1.21396529e+01,  5.13847568e+01,  9.70481539e+03,
                   1.19187283e+02,  2.12183001e+04,  4.66885306e+01,
                   1.81110095e+04,  6.27009428e+01,  6.02838500e+01,
                   4.45961995e+01,  7.58412536e+01,  5.01611717e+02,
                   1.21957866e+02,  6.02392773e+01,  6.17263207e+01,
                   4.97868582e+02,  4.08788306e+01,  6.93354033e+01,
                   2.99934400e+01,  6.97255538e+00,  5.76829061e+03,
                   1.03235608e+01,  1.58235294e+02,  1.24135138e+02,
                   2.28596277e+01,  1.69792325e+02,  1.01066449e+03,
                   1.61421856e+02,  2.67458375e+03,  1.03364083e+02,
                   1.58012945e+02,  3.25906914e+02,  2.01554110e+01,
                   1.41694718e+02,  6.13487630e+01,  6.89998982e+01,
                   6.16380581e+02,  7.54942584e+02,  3.50562326e+02,
                   8.33187692e+01,  5.12648890e+03,  1.23397812e+02,
                   5.36707365e+01,  4.09270065e+02,  2.31762605e+03,
                   1.07972146e+03,  1.81336722e+01,  2.94447371e+02,
                   3.48863242e+02,  9.72803171e+03,  1.17137658e+02,
                   1.74008317e+03,  1.32128964e+03,  1.03753468e+01,
                   5.21292323e+00,  2.81913307e+01,  9.79251297e-01,
                   1.77514613e+00, -9.22894950e-02,  3.15519223e-01,
                   3.95818855e-01,  4.03551825e-01, -7.70467590e-01,
                   5.74118863e-01, -3.09128261e-01,  1.26720734e+00,
                   1.40362869e-01, -2.77320172e-01,  2.84869161e-01,
                  -3.48943218e-01,  1.67312787e-01, -2.51293792e-01,
                  -1.41944882e-01, -1.73632877e-01, -2.76698598e-01,
                   3.75444208e+00,  1.18685876e+01, -1.19363787e+00,
                  -1.41704732e-01,  1.12146209e+02,  6.25398394e+00,
                   2.56808027e+02,  1.73030663e+03,  2.03378354e+01,
                   5.91399373e-01,  3.53704605e+01, -2.43886243e+00,
                  -1.90249562e+00,  5.13073975e-01, -4.78152008e-01,
                   1.32014659e+00, -3.62297598e-01,  1.14484590e+00,
                   1.62716851e+00,  1.81218054e-01,  1.19156224e+00,
                  -5.66967129e-01, -8.03936999e-01,  4.49869907e-01,
                  -3.68889012e-01, -1.62675119e-01, -4.31521084e-01,
                  -2.25167835e-01,  3.58840944e-01,  5.13611491e-01,
                   6.62413738e-01,  1.47684592e-01, -1.14568522e-01,
                  -4.51471548e-01, -5.10794526e-01]])
        • tree_size
          (chain, draw)
          float64
          7.0 23.0 7.0 7.0 ... 15.0 31.0 15.0
          array([[ 7., 23.,  7.,  7.,  7., 15.,  7., 15., 15., 15., 15., 15., 15.,
                   7., 15., 15.,  7.,  7., 23., 15., 15., 31., 31., 15., 15., 31.,
                  15., 15., 15., 15., 31., 15., 31., 15., 31., 15., 23., 15., 15.,
                  15., 15., 31., 31., 31., 31., 15., 31., 15., 31., 31.,  7., 15.,
                  31., 31., 15., 15., 31.,  7.,  7., 15., 15.,  7.,  7., 15., 15.,
                   7.,  7.,  7., 15., 15., 15., 15., 31.,  7., 15.,  7., 15., 15.,
                  15., 15.,  7.,  7., 31., 31., 15., 15., 15., 15., 15., 31., 15.,
                  31., 31., 15., 15.,  7.,  7.,  7., 15., 31., 31., 15., 15., 15.,
                   7., 23.,  7.,  7.,  7.,  7.,  3.,  7.,  7.,  7.,  3.,  7., 15.,
                   7., 15., 31., 15., 15.,  7., 15., 15., 15., 15., 31., 15., 15.,
                  15., 31., 15., 15., 31., 15.,  7.,  7.,  7.,  7., 11.,  7.,  1.,
                   3.,  1., 15.,  3.,  4.,  3.,  7.,  3., 17.,  3.,  3., 15.,  7.,
                  15., 31., 31., 15., 15., 15., 15.,  7.,  7., 15., 15., 15., 15.,
                  31., 31., 15., 15., 15., 15., 15., 15., 15.,  7.,  7.,  9., 23.,
                   3.,  3.,  7.,  7.,  7.,  7., 15.,  7., 15., 31., 15., 15., 15.,
                  31., 31., 31., 31., 31., 31., 31., 31., 31., 31., 15., 15., 15.,
                  11., 15., 15., 15., 15., 39., 15., 15., 31., 15., 15.,  7., 15.,
                  15.,  7., 31.,  7., 15., 15., 15.,  3.,  3.,  7.,  7.,  3.,  3.,
                   3., 15.,  7., 15.,  3.,  3.,  3., 18.,  3.,  1.,  3.,  3.,  7.,
                  31.,  3.,  3.,  7.,  7., 11.,  7.,  7., 15., 15., 15., 15., 15.,
                   7., 15., 15., 15., 31., 15., 31., 31., 15., 15., 15., 15., 15.,
                  15.,  7., 15., 15., 15.,  7.,  7., 15., 15., 15., 15., 31., 15.,
                  15., 15., 15., 31., 15.,  7., 23.,  7.,  3.,  7.,  7.,  7.,  3.,
                   3.,  5.,  3.,  3., 15., 23., 15.,  7.,  7.,  7.,  7.,  3.,  7.,
                   7., 15., 31., 15., 15.,  7.,  7.,  7., 31., 15., 15., 15., 31.,
                  31., 31., 31., 31., 31., 31., 15., 15., 31., 15., 31., 15., 15.,
                  31., 31., 31., 15., 31., 15., 31., 15., 31., 15., 15., 15.,  3.,
                  15., 15., 15., 31., 15., 15., 15., 15., 15., 23., 15.,  7.,  7.,
                   7., 23.,  7.,  6., 23., 15.,  7., 31., 15., 15., 15., 15., 15.,
                  15., 31., 15., 15., 15., 15., 31., 31., 15., 15., 15., 31., 15.,
                  15.,  7., 15.,  7., 15., 31., 15., 15.,  7.,  7.,  7., 15.,  7.,
                  15.,  7.,  3.,  7.,  7.,  7.,  7.,  7.,  7., 15., 15., 15.,  7.,
                  15., 15., 31., 31., 31., 31., 31., 31., 31., 15., 31., 31., 15.,
                   7., 15., 15., 31., 15., 15., 15., 15., 63., 15., 15., 15., 15.,
                  15., 31., 31., 31., 15., 15., 15., 15., 31., 15.,  7., 15.,  7.,
                  23.,  3., 31., 15., 15., 15., 15., 15., 15., 15., 15., 31., 15.,
                  31., 31., 31., 31., 15., 15.,  7., 15., 15., 15., 15., 15., 31.,
                  15., 15., 31., 15., 15., 15., 15., 31., 15., 15., 15., 31., 31.,
                   7., 31.,  7.,  7.,  1.,  3.],
                 [ 7.,  3.,  1.,  3.,  3.,  1.,  5.,  7.,  3.,  7., 31., 15., 15.,
                  15., 31., 31., 15., 31., 15., 31., 31., 15., 31., 15., 15., 15.,
                  15., 15., 15., 19., 15., 15., 31., 15., 15., 15.,  7.,  7.,  7.,
                   7.,  7.,  7.,  7.,  7.,  7.,  7., 15., 31., 31., 15., 15., 15.,
                  15., 15., 15., 15., 15.,  7., 15., 15.,  7.,  7., 31., 31., 15.,
                  15., 15.,  7.,  7.,  7.,  7.,  7., 15., 15., 15., 31., 31., 31.,
                  15., 31., 31., 15., 15., 15., 31., 15., 15., 31., 31., 31., 31.,
                  31., 15., 15., 15.,  7.,  7.,  7.,  7.,  7.,  7., 15.,  7., 15.,
                  15., 15., 15., 15.,  7., 15., 15., 15., 15.,  7., 15.,  7., 15.,
                   7.,  1., 23.,  7.,  7., 31.,  7., 15., 15.,  7.,  7.,  7.,  7.,
                  15.,  7., 15., 15., 15., 15.,  7., 15.,  7.,  7.,  7., 15., 31.,
                   7., 15.,  7., 15., 31., 31., 31., 31., 31., 31., 15., 15., 15.,
                  15., 31., 15., 15., 15., 15., 15., 15., 15., 15., 31., 31., 15.,
                  15., 31., 15., 15., 15., 15., 15., 31., 31., 31., 15., 31., 15.,
                  15., 31., 15., 15., 15., 31., 15., 15., 15., 15., 15., 15., 23.,
                   7.,  7.,  3.,  7., 15., 15., 15., 15., 15., 31., 15., 15., 15.,
                  15., 15., 15., 31., 31., 31., 15., 31., 31., 15., 15., 15., 15.,
                  31., 15., 31., 15.,  7., 15., 31., 31., 15.,  7.,  7., 15.,  7.,
                  15., 31., 31., 31., 31.,  7.,  7., 31.,  3.,  7.,  7.,  7.,  7.,
                  15., 15., 31., 15., 15., 15., 31., 31.,  7., 15.,  7.,  7., 31.,
                   7.,  7., 23., 15.,  7., 15.,  7.,  3.,  3.,  7., 31., 31.,  7.,
                  11.,  7.,  7.,  7., 31., 31., 15.,  7.,  7., 31.,  7.,  7.,  7.,
                   7., 15., 15., 31., 31., 15., 15., 15., 15., 15., 15.,  7., 31.,
                  15., 15., 15.,  7., 31., 15., 15., 15., 15., 23., 31., 15., 15.,
                  15., 15.,  7.,  3.,  7., 15.,  7., 15.,  3., 15., 23.,  7., 15.,
                  15., 15., 15., 15.,  3.,  7.,  1.,  3.,  3.,  3.,  6.,  3.,  3.,
                   7.,  7.,  7.,  7.,  7.,  3.,  3., 15.,  7.,  3.,  7.,  7., 15.,
                   7., 31.,  7.,  7.,  7.,  7., 15.,  1., 15.,  7.,  3.,  1.,  9.,
                   3.,  3.,  3.,  1.,  3.,  5.,  3.,  6.,  3.,  3.,  6.,  1., 15.,
                   1.,  1.,  5.,  1.,  1.,  1.,  1.,  3.,  3.,  1.,  1.,  1., 27.,
                   1.,  1.,  2.,  1.,  3.,  1.,  3.,  1.,  3.,  1.,  1.,  1.,  1.,
                   1.,  1.,  1.,  1.,  1.,  1.,  1.,  3.,  1.,  1.,  1.,  1.,  3.,
                   3.,  1.,  3.,  1.,  1.,  1.,  1.,  1.,  3.,  3.,  1.,  3.,  3.,
                   1.,  3.,  1.,  1.,  1.,  3.,  3.,  1.,  1., 15.,  3.,  1.,  3.,
                   5.,  7., 15.,  7.,  7., 31., 15., 15., 15.,  7., 15.,  7., 23.,
                   3., 15., 15., 15., 15., 15., 15., 15., 15.,  3.,  7.,  7., 31.,
                   7.,  7.,  7., 15.,  7.,  7.,  7., 31.,  7.,  7., 15., 31., 31.,
                   7., 31.,  7.,  3., 15., 15.,  7.,  7., 15.,  7., 15., 31., 23.,
                   7.,  7., 15., 15., 31., 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, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, False, False, False, False, False, False, False,
                  False, False, 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,  True, 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,
                   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,  True, 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,  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,  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,  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,  True,  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,
                   True, False,  True, False, False,  True, False, False, False,
                  False,  True, False, False, False, False, False, False, False,
                  False, False, False, False, False,  True, False,  True, False,
                   True, False, False, False, False, False, False, False, False,
                  False, False, False, False, False,  True, False, False, False,
                  False, False,  True, False,  True, False, False, False, False,
                  False, False, False, False, False, False, False,  True, False,
                  False, False,  True,  True, False, False, False,  True, False,
                   True,  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,  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]])
        • mean_tree_accept
          (chain, draw)
          float64
          0.968 0.9316 ... 0.9912 0.9664
          array([[9.68032085e-001, 9.31630204e-001, 8.07449576e-001,
                  9.61140741e-001, 8.86518335e-001, 9.71293562e-001,
                  9.81188776e-001, 9.84199600e-001, 9.35830218e-001,
                  9.42818108e-001, 9.70378804e-001, 9.69211777e-001,
                  9.84525174e-001, 8.94086151e-001, 9.95622173e-001,
                  9.49383160e-001, 9.56127176e-001, 8.43583801e-001,
                  1.31732741e-001, 9.73272477e-001, 9.20780965e-001,
                  9.60676149e-001, 9.36653625e-001, 9.69211140e-001,
                  9.87690386e-001, 1.00000000e+000, 9.99949943e-001,
                  9.95723762e-001, 9.41549772e-001, 6.17533623e-001,
                  9.78377054e-001, 7.94641966e-001, 9.84320836e-001,
                  9.96393038e-001, 9.98387729e-001, 9.57342768e-001,
                  9.47609845e-001, 9.90032763e-001, 9.71539229e-001,
                  9.05856664e-001, 9.71276543e-001, 9.66736978e-001,
                  9.72887495e-001, 9.95551425e-001, 9.97739459e-001,
                  9.89416105e-001, 9.75099460e-001, 9.86536502e-001,
                  9.88188984e-001, 9.93658967e-001, 7.49272785e-001,
                  6.19924976e-001, 9.75026487e-001, 9.80507920e-001,
                  1.00000000e+000, 8.93513862e-001, 9.97503125e-001,
                  9.75478772e-001, 9.97214127e-001, 9.39636917e-001,
                  1.00000000e+000, 9.91572645e-001, 2.49138671e-001,
                  9.63737267e-001, 9.67114011e-001, 9.81483595e-001,
                  9.58198105e-001, 9.36251067e-001, 9.58539971e-001,
                  9.60141330e-001, 8.40864349e-001, 9.84969423e-001,
                  9.79430355e-001, 8.99720890e-001, 8.59572167e-001,
                  8.07181525e-001, 7.39275844e-001, 9.48363628e-001,
                  9.42747595e-001, 9.23290578e-001, 5.70638866e-001,
                  9.10759207e-001, 5.77685541e-001, 9.80867943e-001,
                  9.85436623e-001, 9.83971235e-001, 9.98134209e-001,
                  9.32521106e-001, 9.82562612e-001, 8.81254052e-001,
                  9.37465150e-001, 9.36480635e-001, 9.77221796e-001,
                  9.96332813e-001, 9.70377454e-001, 1.00000000e+000,
                  9.71208923e-001, 5.66372917e-001, 8.08096284e-001,
                  9.69052204e-001, 9.95661768e-001, 9.95811154e-001,
                  9.91451716e-001, 9.75098465e-001, 8.90772316e-001,
                  9.40612552e-001, 1.00000000e+000, 8.30551651e-001,
                  1.38420300e-001, 7.36939176e-001, 1.00000000e+000,
                  9.24401027e-001, 5.94667344e-001, 5.55896698e-001,
                  8.34997371e-004, 1.92587423e-001, 8.15509443e-001,
                  7.55442398e-001, 9.97016251e-001, 7.97663957e-001,
                  9.27841711e-001, 9.83983960e-001, 9.96158225e-001,
                  9.80901454e-001, 1.00000000e+000, 9.99207882e-001,
                  9.55016942e-001, 9.17708485e-001, 9.99970916e-001,
                  8.28382218e-001, 9.86371973e-001, 9.95959755e-001,
                  9.31273733e-001, 9.75585205e-001, 9.94193824e-001,
                  9.97878434e-001, 1.00000000e+000, 7.65874441e-001,
                  9.37414855e-001, 6.80707753e-001, 3.94740290e-001,
                  2.62985361e-001, 3.22827919e-060, 4.96813560e-004,
                  1.42375422e-035, 7.88322687e-007, 8.75667671e-001,
                  5.00000000e-001, 2.01075368e-001, 3.10454336e-005,
                  5.18563035e-001, 1.10405611e-001, 9.50874846e-003,
                  4.29031653e-002, 1.27402437e-001, 2.04079858e-001,
                  9.92703123e-001, 7.60481063e-001, 9.86369179e-001,
                  9.74021501e-001, 9.96192056e-001, 9.80682089e-001,
                  9.85195720e-001, 9.75283340e-001, 9.26142913e-001,
                  1.00000000e+000, 7.08694973e-001, 9.87288631e-001,
                  8.65968710e-001, 9.78324502e-001, 9.84614072e-001,
                  9.66465027e-001, 1.00000000e+000, 9.91582884e-001,
                  9.89743902e-001, 9.96259779e-001, 5.30357533e-001,
                  5.37513940e-001, 8.15660120e-001, 8.87564142e-001,
                  6.91602304e-001, 5.85240426e-001, 3.38796142e-001,
                  6.77741697e-001, 6.69155648e-001, 8.25396103e-001,
                  2.04860170e-002, 9.86182064e-001, 8.91799709e-001,
                  8.69228858e-001, 7.61502252e-001, 9.92007029e-001,
                  9.99101614e-001, 6.95231189e-001, 9.98598216e-001,
                  9.26785698e-001, 8.96115281e-001, 9.20583794e-001,
                  8.63517927e-001, 9.77394578e-001, 9.93385173e-001,
                  8.57533069e-001, 9.96061830e-001, 9.91788531e-001,
                  9.90094138e-001, 9.89970991e-001, 9.93781511e-001,
                  7.91746818e-001, 9.97467109e-001, 9.37627452e-001,
                  9.88168930e-001, 9.23279691e-001, 9.92825494e-001,
                  9.72262727e-001, 9.25661667e-001, 9.99909676e-001,
                  9.26933974e-001, 9.67291549e-001, 9.95398884e-001,
                  9.78765050e-001, 2.57183197e-001, 9.93100589e-001,
                  9.85408126e-001, 9.62711465e-001, 7.62163740e-001,
                  9.10250752e-001, 9.91870349e-001, 9.47009713e-001,
                  7.42755976e-001, 1.39181705e-001, 2.50215173e-001,
                  1.16933676e-001, 9.44873361e-001, 3.33333452e-001,
                  2.00860680e-001, 7.87848943e-001, 8.92565910e-001,
                  4.05810647e-001, 2.81827364e-001, 4.89002190e-002,
                  2.81962060e-001, 1.86903079e-001, 5.68434921e-001,
                  9.02018527e-007, 1.45226471e-002, 8.70142655e-006,
                  1.42867736e-001, 1.60701394e-002, 7.66600995e-001,
                  1.08827640e-004, 1.30011217e-001, 1.99811089e-003,
                  4.36565716e-001, 9.66707743e-001, 4.25376373e-001,
                  6.96146305e-001, 9.12341057e-001, 9.81403086e-001,
                  7.59452300e-001, 9.95272724e-001, 7.36661001e-001,
                  8.58958408e-001, 8.91250963e-001, 9.87561002e-001,
                  8.63326180e-001, 9.85001743e-001, 9.89378282e-001,
                  9.95361315e-001, 9.99324144e-001, 9.40634205e-001,
                  9.90502583e-001, 9.79301893e-001, 9.78859738e-001,
                  9.90633734e-001, 7.49239561e-001, 9.93326736e-001,
                  9.82082483e-001, 9.69454617e-001, 1.00000000e+000,
                  9.98183169e-001, 5.99491320e-001, 7.70130781e-001,
                  9.98531802e-001, 7.88980635e-001, 9.36243616e-001,
                  9.86553062e-001, 9.92551037e-001, 9.57076411e-001,
                  9.53627190e-001, 9.29876057e-001, 9.64595164e-001,
                  9.17923496e-001, 8.72696885e-001, 7.69850736e-001,
                  3.71808843e-001, 8.61967727e-003, 1.34601149e-001,
                  3.13971015e-002, 4.53453056e-004, 4.26482978e-015,
                  5.70964102e-002, 4.70434918e-007, 7.38895110e-004,
                  5.70055153e-004, 3.81280193e-001, 8.05226750e-001,
                  9.84119886e-001, 9.75388040e-001, 8.64964311e-001,
                  9.96241010e-001, 1.00000000e+000, 2.30062437e-001,
                  9.99943462e-001, 8.49184646e-001, 9.89303794e-001,
                  9.76727328e-001, 9.61843754e-001, 8.25888494e-001,
                  7.90515169e-001, 9.69381620e-001, 8.12298512e-001,
                  9.07903596e-001, 9.22696045e-001, 9.98502033e-001,
                  9.72881106e-001, 9.71950805e-001, 9.91101751e-001,
                  9.97484306e-001, 9.97329167e-001, 6.97030722e-001,
                  1.00000000e+000, 9.70198814e-001, 9.95107462e-001,
                  1.00000000e+000, 4.21345279e-001, 9.92711548e-001,
                  9.19234128e-001, 9.98547829e-001, 9.48688585e-001,
                  9.44234027e-001, 9.63009018e-001, 9.78687098e-001,
                  7.05324206e-001, 9.47599245e-001, 9.95806738e-001,
                  9.72913292e-001, 9.97023998e-001, 8.59521411e-001,
                  9.77688333e-001, 9.63341202e-001, 8.00685135e-001,
                  9.80912060e-001, 9.98487268e-001, 5.49846006e-001,
                  9.94781691e-001, 9.37141146e-001, 9.73657887e-001,
                  9.75178023e-001, 7.16878231e-001, 9.43284375e-001,
                  8.20041853e-001, 7.91001860e-001, 8.24184529e-001,
                  6.78136146e-001, 3.09457849e-001, 8.71387337e-001,
                  8.19618221e-001, 3.92820686e-001, 4.09503427e-002,
                  3.12505644e-001, 9.63251208e-001, 8.20949111e-001,
                  7.43198660e-001, 8.71162693e-001, 9.85436079e-001,
                  9.24535832e-001, 9.91950956e-001, 9.66144790e-001,
                  9.84845644e-001, 9.76285251e-001, 9.45571888e-001,
                  9.16403010e-001, 9.83180426e-001, 9.21693991e-001,
                  9.64940831e-001, 9.59604341e-001, 9.96371820e-001,
                  9.98979771e-001, 9.52305468e-001, 9.88282479e-001,
                  9.99458178e-001, 9.43638768e-001, 8.28843061e-001,
                  9.15551109e-001, 9.93706288e-001, 9.79975038e-001,
                  9.44971780e-001, 8.78491123e-001, 8.13019253e-001,
                  3.13527786e-001, 9.56911039e-001, 6.39243342e-001,
                  9.66200269e-001, 8.04976123e-001, 2.08933563e-001,
                  9.89683859e-002, 2.88165385e-001, 5.47131075e-001,
                  4.34195286e-001, 8.73796651e-001, 9.87866260e-001,
                  9.79003423e-001, 9.78868621e-001, 9.95616742e-001,
                  8.53791526e-001, 8.89117305e-001, 1.00000000e+000,
                  9.57211360e-001, 9.89164244e-001, 9.24231980e-001,
                  9.80156762e-001, 9.94675834e-001, 9.91561543e-001,
                  9.75579070e-001, 9.61802810e-001, 9.85894473e-001,
                  9.86170188e-001, 8.76038901e-001, 9.84673104e-001,
                  8.00494298e-001, 9.86578929e-001, 9.35641470e-001,
                  9.91411545e-001, 9.34924032e-001, 9.81880295e-001,
                  8.35540830e-001, 8.89272248e-001, 9.93232897e-001,
                  9.20562338e-001, 9.62010570e-001, 9.91580781e-001,
                  9.88532356e-001, 9.75772753e-001, 9.87117930e-001,
                  9.81626150e-001, 9.92030739e-001, 9.86752683e-001,
                  9.54050688e-001, 9.71271724e-001, 9.85447953e-001,
                  9.89143160e-001, 9.56698883e-001, 1.00000000e+000,
                  6.38244611e-001, 6.21465825e-001, 1.00000000e+000,
                  4.16945263e-001, 9.32000918e-001, 9.96789143e-001,
                  9.98661998e-001, 9.61272395e-001, 6.53343863e-001,
                  9.26739341e-001, 9.54734960e-001, 6.60040986e-001,
                  9.67143826e-001, 9.45933861e-001, 9.93311512e-001,
                  9.94854019e-001, 9.12140113e-001, 9.98222453e-001,
                  9.99397493e-001, 9.62694888e-001, 1.00000000e+000,
                  8.84325550e-001, 1.00000000e+000, 9.32423141e-001,
                  9.87577804e-001, 9.96710278e-001, 8.19892872e-001,
                  9.96307070e-001, 9.93249378e-001, 1.00000000e+000,
                  9.69161107e-001, 9.81764920e-001, 9.96937902e-001,
                  9.99230557e-001, 9.83612125e-001, 9.76148187e-001,
                  8.88730417e-001, 9.26377341e-001, 9.93575832e-001,
                  9.06601196e-001, 9.56613958e-001, 6.69570063e-001,
                  8.78467439e-001, 7.63135864e-001, 9.63294594e-001,
                  1.39603433e-026, 9.35288114e-002],
                 [8.31607631e-001, 1.18047671e-001, 1.11318790e-022,
                  2.19453381e-002, 3.33335941e-001, 1.00000000e+000,
                  5.28310952e-001, 2.30632222e-001, 5.41790531e-001,
                  9.78192295e-001, 5.06991818e-001, 9.67665223e-001,
                  9.38287990e-001, 9.68937585e-001, 9.90495530e-001,
                  9.68510832e-001, 9.81591285e-001, 9.87185722e-001,
                  8.90468027e-001, 9.35704963e-001, 9.83203428e-001,
                  9.94473054e-001, 9.10589560e-001, 9.87634620e-001,
                  9.96405802e-001, 9.89460217e-001, 8.76342754e-001,
                  1.00000000e+000, 9.95757490e-001, 7.54216319e-001,
                  9.79265307e-001, 9.61087418e-001, 6.70597749e-001,
                  9.49220653e-001, 9.93842436e-001, 9.14934138e-001,
                  9.54559847e-001, 8.64087926e-001, 8.75616330e-001,
                  8.85398874e-001, 8.39934442e-001, 9.14725409e-001,
                  9.88599250e-001, 9.65429710e-001, 6.39664450e-001,
                  7.61808669e-001, 9.92019022e-001, 6.93277531e-001,
                  9.54052586e-001, 1.00000000e+000, 9.95929640e-001,
                  9.93878818e-001, 9.91026685e-001, 8.94052264e-001,
                  9.83024009e-001, 9.89627783e-001, 9.49806665e-001,
                  1.00000000e+000, 9.93486511e-001, 9.72269041e-001,
                  9.02485102e-001, 9.82902309e-001, 9.01381352e-001,
                  9.97258807e-001, 9.90450217e-001, 9.85128862e-001,
                  9.87351962e-001, 8.89894014e-001, 8.88705349e-001,
                  6.12919398e-001, 9.85966233e-001, 8.51218457e-001,
                  9.72912233e-001, 8.86864767e-001, 1.00000000e+000,
                  8.82689993e-001, 9.68047372e-001, 9.87743621e-001,
                  8.39870556e-001, 9.74441701e-001, 9.68676815e-001,
                  9.95143672e-001, 9.98166877e-001, 9.56721528e-001,
                  9.89846900e-001, 9.98110443e-001, 9.36613531e-001,
                  9.99962848e-001, 9.35247586e-001, 9.97134429e-001,
                  9.82153415e-001, 9.79675661e-001, 9.75630770e-001,
                  9.65467809e-001, 9.06426422e-001, 9.97098849e-001,
                  7.75419310e-001, 9.82527228e-001, 9.58684659e-001,
                  9.92841240e-001, 9.73340527e-001, 9.89230929e-001,
                  4.84668717e-001, 9.99109128e-001, 8.72283456e-001,
                  9.75961719e-001, 9.97935551e-001, 9.83527878e-001,
                  9.36867452e-001, 9.87232694e-001, 9.76292318e-001,
                  9.38554000e-001, 9.72778252e-001, 8.80998196e-001,
                  9.66514472e-001, 9.74319747e-001, 8.54141486e-001,
                  8.57768559e-001, 4.42227555e-041, 7.65856148e-001,
                  9.78371201e-001, 8.72860007e-001, 6.57749689e-001,
                  1.00000000e+000, 9.99275201e-001, 8.64600936e-001,
                  8.30050667e-001, 9.80062930e-001, 5.74601589e-001,
                  1.00000000e+000, 9.46624347e-001, 9.65786433e-001,
                  9.26543550e-001, 9.90107538e-001, 9.17410685e-001,
                  9.93525583e-001, 9.64630295e-001, 9.29008516e-001,
                  9.13262641e-001, 8.33969808e-001, 7.14285714e-001,
                  8.72573986e-001, 9.63326199e-001, 7.79417679e-001,
                  9.85022420e-001, 1.00000000e+000, 9.20344425e-001,
                  7.82512751e-001, 9.59529040e-001, 9.56309347e-001,
                  1.00000000e+000, 9.95312224e-001, 9.84165167e-001,
                  8.82263907e-001, 9.71353066e-001, 9.94032800e-001,
                  9.76044260e-001, 4.88962598e-001, 9.87229338e-001,
                  9.73889563e-001, 8.73530289e-001, 9.48388136e-001,
                  9.82903129e-001, 9.87764262e-001, 5.74299876e-001,
                  9.95755153e-001, 9.81374848e-001, 7.27452673e-001,
                  9.17189798e-001, 5.05267675e-001, 9.78559199e-001,
                  9.87053243e-001, 9.95603381e-001, 9.86044924e-001,
                  9.71295571e-001, 9.88491587e-001, 9.27617517e-001,
                  8.74466100e-001, 9.88763385e-001, 9.83165537e-001,
                  9.65012002e-001, 9.97909851e-001, 9.99507328e-001,
                  9.92848670e-001, 9.92176498e-001, 9.96346113e-001,
                  9.78859805e-001, 9.60725604e-001, 9.99710803e-001,
                  9.94955825e-001, 9.94254386e-001, 9.96784170e-001,
                  9.83665147e-001, 9.95457715e-001, 8.94857843e-001,
                  9.59954923e-001, 1.00751325e-002, 3.39414943e-001,
                  7.97698643e-004, 2.88048029e-001, 4.41627410e-001,
                  9.88043941e-001, 9.99842973e-001, 5.95916619e-001,
                  9.90057301e-001, 9.55707452e-001, 9.89210139e-001,
                  9.98509238e-001, 8.74388008e-001, 9.94173485e-001,
                  9.21828283e-001, 8.76169929e-001, 9.91922750e-001,
                  9.64321980e-001, 9.57780511e-001, 9.92914681e-001,
                  8.55836590e-001, 9.86160536e-001, 9.83434418e-001,
                  9.88212885e-001, 9.73804058e-001, 9.96793267e-001,
                  9.88823849e-001, 9.26024190e-001, 9.90552707e-001,
                  6.43921983e-001, 8.14169876e-001, 9.83814069e-001,
                  8.92247587e-001, 9.93056797e-001, 9.64640729e-001,
                  9.71608451e-001, 9.02198391e-001, 9.37757498e-001,
                  9.21179440e-001, 9.99100151e-001, 9.74285394e-001,
                  9.96705919e-001, 9.97636202e-001, 9.13391566e-001,
                  8.63682312e-001, 1.58299791e-005, 9.65592484e-002,
                  3.85293834e-001, 9.17179885e-001, 9.17422250e-001,
                  8.97563715e-001, 8.79448596e-001, 8.19275780e-001,
                  9.73299568e-001, 6.27438780e-001, 9.53961512e-001,
                  9.95705457e-001, 9.09910381e-001, 9.87999037e-001,
                  9.95320787e-001, 2.19421858e-001, 9.59407946e-001,
                  8.87944541e-001, 4.91881721e-001, 1.00000000e+000,
                  4.16014763e-001, 2.62187435e-001, 7.49083133e-001,
                  8.93022447e-001, 9.69330973e-001, 8.49878086e-001,
                  4.47535283e-001, 2.80435869e-001, 6.25718741e-001,
                  9.20402435e-001, 9.13089777e-001, 1.00000000e+000,
                  9.64280283e-001, 9.84543487e-001, 9.89527261e-001,
                  3.25912212e-001, 9.42024802e-001, 9.74267814e-001,
                  6.68878062e-001, 9.93658693e-001, 9.75518222e-001,
                  9.01959586e-001, 9.55398941e-001, 6.51140011e-001,
                  6.97038803e-001, 6.84586633e-001, 8.85210585e-001,
                  9.86880316e-001, 9.90957251e-001, 9.96573208e-001,
                  9.87404922e-001, 9.33465093e-001, 9.91098732e-001,
                  9.58838794e-001, 9.93188535e-001, 9.26196600e-001,
                  9.86788891e-001, 9.82793577e-001, 9.78554524e-001,
                  9.68618652e-001, 9.76002682e-001, 8.97715661e-001,
                  9.95140556e-001, 8.45037562e-001, 9.52207547e-001,
                  9.97103410e-001, 9.96022657e-001, 9.79783241e-001,
                  9.92339295e-001, 9.39686543e-001, 1.00000000e+000,
                  9.80929701e-001, 7.63306308e-001, 4.54194210e-001,
                  1.35399959e-002, 8.54362526e-001, 6.26949269e-001,
                  9.93180493e-001, 9.98981929e-001, 8.16702453e-001,
                  9.22674076e-001, 9.17520938e-001, 9.71238560e-001,
                  9.66940837e-001, 9.36190033e-001, 9.83955333e-001,
                  7.32935145e-001, 8.87955702e-001, 2.75157613e-005,
                  4.06938030e-001, 1.37782029e-003, 5.19077695e-005,
                  6.67126027e-001, 5.85327660e-005, 6.43367990e-005,
                  8.80459157e-005, 2.38609878e-001, 1.24387994e-001,
                  7.08188296e-001, 7.64581142e-001, 6.83798569e-001,
                  7.69991420e-001, 5.93214505e-001, 4.57077040e-001,
                  3.51465022e-001, 9.67215306e-001, 5.72434965e-001,
                  3.91695140e-001, 9.74461693e-001, 9.73396444e-001,
                  7.62047510e-001, 9.57135986e-001, 6.69585877e-001,
                  8.89379570e-001, 7.55039612e-001, 1.60149314e-001,
                  9.94946444e-001, 2.90656330e-012, 6.26107861e-001,
                  5.19456175e-002, 9.01173644e-001, 1.11536831e-005,
                  6.90000847e-005, 7.07536137e-003, 1.51624402e-004,
                  2.14682517e-001, 6.90668828e-025, 3.03608670e-003,
                  3.56866990e-004, 3.36869986e-016, 5.39753219e-002,
                  1.14121791e-001, 1.20722111e-002, 2.68770268e-001,
                  2.04422271e-016, 5.73023597e-007, 1.23749009e-006,
                  1.74585817e-011, 2.00015918e-001, 6.13986619e-031,
                  6.13491752e-041, 1.18242435e-067, 1.62447313e-032,
                  8.67344575e-009, 5.03097116e-019, 1.58022550e-038,
                  1.20537074e-030, 1.52080258e-020, 5.80320930e-009,
                  5.34337613e-006, 4.82929444e-023, 1.51879368e-010,
                  1.72830692e-052, 1.79930447e-003, 5.28967266e-021,
                  4.20895169e-014, 5.87931254e-028, 1.01509506e-011,
                  4.28663647e-020, 1.15494700e-033, 1.42167202e-218,
                  1.08236031e-053, 6.89309525e-027, 1.55811502e-027,
                  6.00374327e-217, 1.76420661e-018, 7.72710719e-031,
                  9.41921073e-014, 9.37254798e-004, 5.03968319e-003,
                  3.28499357e-005, 1.90232677e-069, 1.22685864e-054,
                  1.18083664e-010, 3.15237496e-016, 2.20902631e-016,
                  7.85920302e-071, 6.47670813e-007, 1.28691257e-045,
                  2.37601896e-069, 2.88686042e-142, 1.76447783e-009,
                  2.90245662e-062, 1.21157715e-010, 1.52963793e-006,
                  2.03852002e-268, 9.35070228e-004, 6.33933703e-004,
                  6.53308494e-037, 1.33451711e-005, 2.56455011e-054,
                  4.91015588e-024, 1.80413549e-178, 4.55389974e-021,
                  1.58972008e-004, 1.33243556e-008, 1.32779651e-128,
                  1.17991537e-022, 1.48996541e-001, 1.34202733e-051,
                  2.42760335e-002, 7.40791200e-003, 5.73716157e-001,
                  6.38623403e-002, 7.47091961e-001, 6.00239517e-001,
                  4.23528406e-001, 9.94391225e-001, 8.39765910e-001,
                  8.90479035e-001, 8.15285118e-001, 9.85524720e-001,
                  7.09815988e-001, 9.94795043e-001, 7.00002580e-001,
                  9.21468102e-001, 9.54221170e-001, 9.52680803e-001,
                  9.82559845e-001, 9.20733591e-001, 9.89411075e-001,
                  1.00000000e+000, 9.79966572e-001, 1.00000000e+000,
                  3.50524586e-001, 2.48890553e-001, 8.61168810e-001,
                  9.66069591e-001, 1.09310937e-001, 7.92894920e-001,
                  5.19132297e-001, 5.72605488e-001, 1.84888122e-001,
                  9.25237261e-001, 7.46153946e-001, 9.40279320e-001,
                  1.00000000e+000, 7.27552544e-001, 9.89229425e-001,
                  8.94471220e-001, 8.44421389e-001, 6.80160277e-001,
                  6.48456431e-001, 9.15691366e-001, 4.18203657e-001,
                  9.16228339e-001, 9.51461528e-001, 8.64733657e-001,
                  9.65868694e-001, 9.94454296e-001, 9.36387533e-001,
                  9.84778246e-001, 9.76179542e-001, 8.02857872e-001,
                  8.55552366e-001, 9.47965105e-001, 9.82086709e-001,
                  9.91229742e-001, 9.66360813e-001]])
        • lp
          (chain, draw)
          float64
          -51.92 -50.57 ... -56.73 -58.36
          array([[-51.91665759, -50.56775853, -52.19800849, -52.21974618,
                  -53.3420215 , -55.59382132, -54.74545138, -55.055417  ,
                  -58.2331127 , -56.50119657, -58.03525824, -57.7008949 ,
                  -55.223101  , -55.86131088, -55.05558026, -56.76063724,
                  -51.17129068, -51.48010069, -56.35027654, -58.88378034,
                  -61.58590773, -59.44696319, -69.0918996 , -63.02749529,
                  -62.80311441, -60.81918395, -59.82614801, -56.01628544,
                  -54.52675127, -59.39513391, -59.91122298, -60.67353723,
                  -59.61098542, -61.08538467, -63.08738026, -61.91602109,
                  -63.90940822, -59.83179848, -56.35095756, -66.03528067,
                  -62.00133641, -65.02740605, -63.79910221, -61.33885848,
                  -61.51587057, -63.79034664, -62.14053988, -62.24832896,
                  -65.28292803, -58.34289423, -59.91302189, -62.91222768,
                  -64.65220032, -58.54999314, -54.21186273, -60.21917596,
                  -56.35808439, -55.02733749, -52.78179695, -56.94633732,
                  -55.45120963, -53.73265869, -54.28147166, -56.90422839,
                  -53.80611919, -53.74666715, -52.69895856, -54.44692189,
                  -55.78369688, -58.55357111, -54.74275138, -57.14729928,
                  -53.10755404, -55.80472156, -49.87671205, -53.14000545,
                  -52.4842398 , -54.86652915, -54.82879827, -52.03125183,
                  -50.27406152, -51.85318527, -60.68376044, -60.42315522,
                  -61.86286379, -61.93779628, -60.14527257, -59.10759675,
                  -62.7544117 , -64.07362945, -62.4015889 , -63.60241707,
                  -61.66036408, -62.54991802, -53.16585977, -51.82144413,
                  -51.81119189, -54.484284  , -60.70414504, -62.23210602,
                  -62.19066793, -58.27564769, -56.07965109, -53.17835472,
                  -49.89588271, -50.02782802, -51.09060836, -55.41897402,
                  -55.3524674 , -54.34150015, -50.68442702, -49.03367795,
                  -50.76537652, -49.53949511, -49.53949511, -49.53949511,
                  -51.82127783, -54.43085303, -54.60796774, -57.95442257,
                  -59.09550483, -60.47584447, -58.26224553, -61.26376622,
                  -57.82755082, -58.24338631, -64.21163694, -63.75307601,
                  -62.93012102, -58.82039463, -58.77329999, -55.53854818,
                  -58.48916139, -62.72699606, -64.29569621, -53.67386726,
                  -50.53411379, -50.21479658, -48.90038461, -46.73629537,
                  -46.08534844, -44.41818016, -44.41818016, -44.41818016,
                  -44.41818016, -44.41818016, -44.08972874, -44.15627311,
                  -44.15627311, -44.15627311, -47.19920009, -45.95788812,
                  -45.95788812, -45.95788812, -50.62287236, -56.81287028,
                  -57.82425426, -57.94665952, -56.87146266, -56.93569079,
                  -59.95499214, -58.81582173, -57.35079063, -58.68959522,
                  -57.49777783, -57.25976952, -61.22801195, -57.8221699 ,
                  -61.80567179, -61.14904862, -64.68066189, -56.10947121,
                  -57.33603841, -58.12837546, -57.35863378, -57.28259899,
                  -52.41465008, -50.17773133, -50.69419084, -49.44172965,
                  -49.40823578, -50.63295682, -49.07131436, -48.9847204 ,
                  -50.28879268, -48.00984331, -54.51543092, -54.44387759,
                  -53.20929619, -55.69468044, -60.77927389, -62.04891729,
                  -59.20597943, -59.00905027, -59.41142481, -58.97582939,
                  -60.11396187, -62.89623811, -65.27734463, -62.86293644,
                  -58.52091818, -64.49177759, -63.51051166, -61.0773281 ,
                  -60.53390484, -58.49557415, -56.09959081, -58.05835362,
                  -56.75177404, -61.07568691, -57.14630116, -59.70006999,
                  -60.30344417, -65.54645999, -73.9994647 , -66.6037724 ,
                  -59.79988174, -56.58168165, -55.03643696, -55.10874762,
                  -64.81487514, -59.48550534, -54.32776175, -52.70580421,
                  -55.58263559, -56.10269837, -55.97407526, -52.64237307,
                  -47.41138635, -47.41138635, -46.31433404, -46.11336668,
                  -44.90027129, -44.27602484, -46.44451524, -48.2354552 ,
                  -47.21325849, -45.92765528, -45.92765528, -45.92765528,
                  -45.92765528, -45.78728531, -45.09797708, -45.09797708,
                  -50.43412287, -50.43412287, -47.71702798, -47.71702798,
                  -47.40662288, -47.40662288, -47.40662288, -47.40662288,
                  -50.12370759, -49.2149257 , -49.89335718, -53.33735412,
                  -54.14698229, -54.43940936, -56.59984104, -56.14809569,
                  -56.6063295 , -55.99588742, -59.71471474, -61.49671792,
                  -59.39378622, -66.07653621, -64.74953419, -62.58290019,
                  -59.51139012, -59.84647206, -59.64871374, -57.68648225,
                  -61.77206356, -53.51329291, -56.41319595, -54.08421816,
                  -55.50712501, -57.90833439, -52.90092899, -51.9206097 ,
                  -55.18788777, -59.16492924, -57.80355336, -58.40278598,
                  -59.26811062, -59.65376716, -56.76816485, -62.66457901,
                  -59.48596617, -59.81922639, -50.70863795, -51.24312072,
                  -48.01841112, -46.42420271, -44.5550938 , -44.5550938 ,
                  -44.5550938 , -48.2737449 , -48.2737449 , -48.2737449 ,
                  -48.2737449 , -48.2737449 , -48.2737449 , -48.2737449 ,
                  -52.80252109, -54.09884951, -54.28871924, -52.70210017,
                  -56.45946209, -54.80170915, -50.42527792, -56.01548717,
                  -54.07155612, -60.4664863 , -57.80483557, -56.30552006,
                  -53.40306918, -53.37392819, -51.67754521, -54.6051975 ,
                  -56.22590217, -55.14150747, -62.26147379, -60.58204243,
                  -66.22737861, -61.42862388, -69.535392  , -67.52707333,
                  -68.07706885, -72.75733483, -62.37369908, -60.85594311,
                  -58.44432665, -56.11764635, -55.01027516, -55.98208978,
                  -62.52357822, -58.18295774, -63.8637575 , -65.41108674,
                  -62.96956059, -61.034383  , -65.07890559, -65.44328168,
                  -60.04510926, -59.94740093, -57.64108344, -57.1708942 ,
                  -57.378972  , -59.76573837, -60.19828266, -63.25271685,
                  -61.56332456, -65.08324083, -64.39014968, -59.24054654,
                  -55.84373467, -54.7307264 , -56.17090404, -55.95163252,
                  -51.92256326, -48.63028162, -49.55009622, -51.45608452,
                  -50.90725308, -49.53463003, -47.9943808 , -46.35297374,
                  -46.35297374, -50.02306349, -53.72490679, -55.07144524,
                  -58.45601713, -58.3526234 , -58.44922881, -59.44813806,
                  -59.54198061, -61.9385318 , -62.70022971, -55.3456025 ,
                  -59.37170657, -61.03452616, -63.71167233, -66.50815804,
                  -65.29207073, -64.34985467, -67.91220094, -64.00466522,
                  -62.03861274, -56.57935578, -52.64914054, -52.13071192,
                  -54.77830036, -53.48861274, -53.77422585, -56.44662515,
                  -52.44964602, -48.57419726, -49.00065505, -53.3590815 ,
                  -53.57773781, -52.97386534, -50.53821954, -48.87464117,
                  -52.1162409 , -52.1162409 , -49.68027138, -51.92342637,
                  -55.42072338, -57.00957265, -55.43046907, -54.41537487,
                  -54.10603185, -53.53723931, -55.01496282, -56.33602904,
                  -57.13856393, -63.07113629, -64.12108077, -65.28705235,
                  -63.34935552, -63.21615623, -62.15674951, -62.76141419,
                  -67.94585153, -64.98314206, -65.41378397, -62.66118788,
                  -62.33266681, -60.4072103 , -62.89403167, -63.37461398,
                  -57.10501253, -63.87284287, -62.57251011, -58.20990397,
                  -62.6853362 , -59.89571281, -59.43972026, -59.08281091,
                  -58.89764557, -57.93119308, -61.04300796, -64.61486068,
                  -64.5388905 , -63.85510791, -57.81624122, -58.23953404,
                  -59.48493436, -56.42101754, -57.89253773, -53.28769441,
                  -52.04857235, -49.54477611, -50.57006114, -50.57911914,
                  -56.42712431, -59.44024458, -58.02292663, -58.29469591,
                  -55.06651553, -59.08348939, -58.18343135, -58.49633229,
                  -57.86307108, -58.67645136, -62.30929633, -61.61236538,
                  -61.57793304, -64.87862277, -64.45807708, -62.08990573,
                  -61.52081583, -57.00640428, -56.97260986, -58.16977416,
                  -60.06617887, -59.5694823 , -60.03035958, -64.90089811,
                  -63.09740278, -60.57548345, -59.12003325, -65.41907568,
                  -62.85651404, -60.19278825, -56.82463348, -57.02057248,
                  -61.38968875, -62.11655558, -60.21649964, -56.10337697,
                  -57.08251235, -53.74040758, -53.75262167, -54.5693098 ,
                  -51.16974325, -45.79810622, -45.79810622, -47.2640827 ],
                 [-46.41386165, -49.49347388, -49.49347388, -49.49347388,
                  -47.67560535, -46.27670134, -47.92467544, -56.27941551,
                  -53.35232265, -52.43233696, -57.54041332, -60.24010434,
                  -58.08611163, -61.3736624 , -58.22663399, -62.46252263,
                  -58.29611488, -57.07560089, -60.0807553 , -62.87803124,
                  -64.36767037, -61.44624791, -61.86362939, -59.74038779,
                  -57.99101989, -55.80102192, -65.92309986, -63.00569308,
                  -57.33001048, -54.39908451, -56.54370435, -54.20707458,
                  -57.39469643, -57.34860241, -55.1161245 , -54.59872431,
                  -53.48141309, -52.82320599, -58.22592055, -51.09572182,
                  -50.78164029, -50.67111219, -50.32897976, -51.87294687,
                  -52.04205383, -55.27193021, -54.09586778, -57.45373121,
                  -59.86915705, -57.80212153, -57.53551392, -54.86029885,
                  -55.91902629, -60.39556043, -63.26626763, -64.20036683,
                  -60.91116835, -58.57714377, -56.84125378, -54.30278364,
                  -57.67734425, -56.82084163, -62.09575204, -61.14262696,
                  -61.17365535, -58.6186762 , -53.60957508, -51.33059084,
                  -50.58934904, -52.27024137, -51.11268296, -53.94711878,
                  -57.20200331, -60.22009322, -60.16246312, -60.59488473,
                  -64.97026381, -61.9680031 , -64.14006413, -66.100367  ,
                  -66.1154562 , -69.63809371, -60.32062872, -64.07158737,
                  -61.4349654 , -63.45303592, -63.30072951, -67.0473801 ,
                  -65.64894392, -65.11673858, -66.48291908, -67.1817707 ,
                  -53.40558526, -53.69504351, -53.9288618 , -51.57431681,
                  -52.92202111, -51.76559477, -53.33737393, -53.41923671,
                  -53.87919053, -52.74780337, -58.39004502, -58.22594894,
                  -64.44659478, -60.36353903, -61.43780767, -62.75553293,
                  -56.67039121, -56.92747059, -54.46466392, -55.98745278,
                  -56.2768584 , -57.31423695, -55.25372525, -55.74279323,
                  -56.54003683, -51.44642481, -51.44642481, -54.23881526,
                  -54.05948399, -52.06315023, -54.30915661, -55.81515018,
                  -53.27692125, -54.65094426, -56.80315955, -52.14370797,
                  -55.87633469, -53.16935647, -56.64470084, -55.1779295 ,
                  -58.32758686, -57.99148466, -60.5823629 , -57.66402199,
                  -55.781462  , -58.05272996, -53.33679227, -49.443456  ,
                  -49.87384596, -55.52214636, -56.22936005, -58.97806591,
                  -58.71808406, -58.3575505 , -60.40110574, -61.32315684,
                  -64.38494614, -63.45013265, -69.35425824, -62.88818484,
                  -60.15026064, -60.4265519 , -56.43525048, -53.72726837,
                  -52.20863461, -55.23412351, -54.41597534, -52.83046215,
                  -56.70979031, -58.22982646, -60.69931749, -56.13781185,
                  -58.03448698, -57.03703222, -52.49473245, -53.57613185,
                  -54.1682582 , -64.26672887, -58.9867921 , -58.02955902,
                  -58.57352565, -57.37094084, -60.90855124, -70.25171626,
                  -69.32317247, -65.01237452, -61.25804718, -59.25150665,
                  -59.77752108, -60.20575399, -61.0193506 , -62.05741125,
                  -59.94770929, -60.45878451, -61.11197039, -63.34475904,
                  -62.26598096, -59.38126108, -60.91843085, -60.21857435,
                  -56.06910725, -54.02295898, -50.98527533, -46.54631668,
                  -46.54631668, -46.22847656, -46.22847656, -50.19950147,
                  -59.31706665, -59.87889316, -55.90528546, -60.55990397,
                  -65.28682741, -61.61051872, -61.10119464, -56.0053337 ,
                  -57.01453796, -56.29806494, -58.97379852, -63.8284274 ,
                  -62.53306395, -58.23373391, -60.49745162, -62.34741289,
                  -61.48878992, -55.11332659, -57.19085979, -56.94125994,
                  -60.15873523, -59.45684945, -58.69529673, -57.41060594,
                  -52.04932417, -55.91963338, -63.83500619, -67.19010278,
                  -60.61713463, -54.00054921, -52.32192137, -53.18769554,
                  -56.85729689, -57.18695724, -61.92722289, -59.40475669,
                  -62.28238638, -62.17483978, -60.15707474, -56.51795849,
                  -49.99958254, -49.99958254, -49.99958254, -48.97717364,
                  -49.54293173, -51.42094447, -53.01064392, -52.18663028,
                  -55.88437889, -58.68515686, -57.7082572 , -61.32358661,
                  -54.25044974, -59.9264316 , -56.94895372, -48.93375527,
                  -52.20598442, -51.01281085, -51.73754886, -55.36877876,
                  -51.93513768, -49.05339265, -52.54777196, -49.90185157,
                  -51.89864877, -51.77497965, -52.17085094, -48.97179528,
                  -48.97179528, -52.9486314 , -54.1805225 , -57.3942867 ,
                  -52.71764766, -53.2037535 , -53.68549131, -53.17402141,
                  -58.09270774, -57.41490665, -61.14120479, -61.50907654,
                  -57.16971005, -54.84027627, -54.1284317 , -55.48326669,
                  -52.33148781, -53.76615823, -55.83287275, -60.82988036,
                  -64.33671057, -61.47636531, -60.72919691, -60.26082735,
                  -58.59395215, -56.53857193, -56.14501885, -55.5259046 ,
                  -57.91681043, -60.83802638, -58.58337846, -61.92882868,
                  -57.32212461, -54.61267259, -58.41195539, -54.20042008,
                  -58.03207936, -58.01062852, -54.89364431, -55.24179913,
                  -56.48266723, -56.00211926, -59.37347268, -58.39270628,
                  -55.53877325, -50.97896747, -50.92810023, -50.92810023,
                  -51.99671122, -53.15676002, -52.83482456, -52.15270835,
                  -54.16843157, -55.1308923 , -55.69919945, -55.302565  ,
                  -56.67998642, -57.75047019, -52.60225708, -52.79545815,
                  -52.14812159, -52.14812159, -48.73685257, -48.73685257,
                  -48.73685257, -47.17570041, -47.17570041, -47.17570041,
                  -47.17570041, -46.25273364, -46.25273364, -48.76961863,
                  -49.66563037, -53.42771989, -49.744092  , -49.40464835,
                  -47.34265378, -49.07410669, -50.01046064, -52.83372329,
                  -55.63701624, -55.69363048, -53.75976503, -55.12338148,
                  -50.08225857, -52.53964108, -48.77095272, -48.11579582,
                  -49.36227138, -47.52737779, -47.52737779, -49.12377466,
                  -49.12377466, -45.03453721, -45.03453721, -45.03453721,
                  -45.03453721, -45.03453721, -45.03453721, -45.03453721,
                  -45.03453721, -45.03453721, -45.03453721, -45.03453721,
                  -45.03453721, -45.03453721, -44.40898493, -44.40898493,
                  -44.40898493, -44.40898493, -44.40898493, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -42.67924006,
                  -42.67924006, -42.67924006, -42.67924006, -44.36605011,
                  -44.36605011, -44.36605011, -49.65132736, -47.36979944,
                  -51.39972938, -47.43566364, -49.41501813, -57.52433554,
                  -54.85061778, -53.55412793, -53.10772835, -54.33688509,
                  -49.96686533, -53.63406672, -51.54403839, -53.86794764,
                  -54.7870552 , -61.09799979, -55.70124471, -57.30675621,
                  -61.61392636, -56.78961887, -57.20121332, -53.52394361,
                  -49.96711676, -55.21034171, -49.38772377, -51.26770026,
                  -50.78758878, -49.6141256 , -49.21809891, -48.59294131,
                  -48.1794015 , -57.4249225 , -54.88634227, -53.79001921,
                  -55.83538884, -52.81092049, -55.35050763, -54.01234933,
                  -51.92203924, -53.66805678, -51.50650096, -49.87354425,
                  -47.54916952, -55.37446261, -55.83015413, -58.19677944,
                  -57.88779   , -54.55792776, -52.1321059 , -58.33251306,
                  -57.34812125, -54.56592787, -51.93891934, -56.24425901,
                  -58.74477306, -58.73530521, -56.72532269, -58.3587961 ]])
        • step_size
          (chain, draw)
          float64
          0.2516 0.2516 ... 0.09828 0.09828
          array([[0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967,
                  0.25156967, 0.25156967, 0.25156967, 0.25156967, 0.25156967],
                 [0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907,
                  0.09827907, 0.09827907, 0.09827907, 0.09827907, 0.09827907]])
        • step_size_bar
          (chain, draw)
          float64
          0.2551 0.2551 ... 0.2271 0.2271
          array([[0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ,
                  0.255105  , 0.255105  , 0.255105  , 0.255105  , 0.255105  ],
                 [0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209,
                  0.22713209, 0.22713209, 0.22713209, 0.22713209, 0.22713209]])
        • depth
          (chain, draw)
          int64
          3 5 3 3 3 4 3 4 ... 5 5 3 3 4 4 5 4
          array([[3, 5, 3, 3, 3, 4, 3, 4, 4, 4, 4, 4, 4, 3, 4, 4, 3, 3, 5, 4, 4, 5,
                  5, 4, 4, 5, 4, 4, 4, 4, 5, 4, 5, 4, 5, 4, 5, 4, 4, 4, 4, 5, 5, 5,
                  5, 4, 5, 4, 5, 5, 3, 4, 5, 5, 4, 4, 5, 3, 3, 4, 4, 3, 3, 4, 4, 3,
                  3, 3, 4, 4, 4, 4, 5, 3, 4, 3, 4, 4, 4, 4, 3, 3, 5, 5, 4, 4, 4, 4,
                  4, 5, 4, 5, 5, 4, 4, 3, 3, 3, 4, 5, 5, 4, 4, 4, 3, 5, 3, 3, 3, 3,
                  2, 3, 3, 3, 2, 3, 4, 3, 4, 5, 4, 4, 3, 4, 4, 4, 4, 5, 4, 4, 4, 5,
                  4, 4, 5, 4, 3, 3, 3, 3, 4, 3, 1, 2, 1, 4, 2, 3, 2, 3, 2, 5, 2, 2,
                  4, 3, 4, 5, 5, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 5, 5, 4, 4, 4, 4, 4,
                  4, 4, 3, 3, 4, 5, 2, 2, 3, 3, 3, 3, 4, 3, 4, 5, 4, 4, 4, 5, 5, 5,
                  5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 5, 4, 4, 3,
                  4, 4, 3, 5, 3, 4, 4, 4, 2, 2, 3, 3, 2, 2, 2, 4, 3, 4, 2, 2, 2, 5,
                  2, 1, 2, 2, 3, 5, 2, 2, 3, 3, 4, 3, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4,
                  5, 4, 5, 5, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 3, 3, 4, 4, 4, 4, 5, 4,
                  4, 4, 4, 5, 4, 3, 5, 3, 2, 3, 3, 3, 2, 2, 3, 2, 2, 4, 5, 4, 3, 3,
                  3, 3, 2, 3, 3, 4, 5, 4, 4, 3, 3, 3, 5, 4, 4, 4, 5, 5, 5, 5, 5, 5,
                  5, 4, 4, 5, 4, 5, 4, 4, 5, 5, 5, 4, 5, 4, 5, 4, 5, 4, 4, 4, 2, 4,
                  4, 4, 5, 4, 4, 4, 4, 4, 5, 4, 3, 3, 3, 5, 3, 3, 5, 4, 3, 5, 4, 4,
                  4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 5, 4, 4, 4, 5, 4, 4, 3, 4, 3, 4, 5,
                  4, 4, 3, 3, 3, 4, 3, 4, 3, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4,
                  5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 4, 3, 4, 4, 5, 4, 4, 4, 4, 6, 4, 4,
                  4, 4, 4, 5, 5, 5, 4, 4, 4, 4, 5, 4, 3, 4, 3, 5, 2, 5, 4, 4, 4, 4,
                  4, 4, 4, 4, 5, 4, 5, 5, 5, 5, 4, 4, 3, 4, 4, 4, 4, 4, 5, 4, 4, 5,
                  4, 4, 4, 4, 5, 4, 4, 4, 5, 5, 3, 5, 3, 3, 1, 2],
                 [3, 2, 1, 2, 2, 1, 3, 3, 2, 3, 5, 4, 4, 4, 5, 5, 4, 5, 4, 5, 5, 4,
                  5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 5, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3,
                  3, 3, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 3, 3, 5, 5, 4, 4,
                  4, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 4, 5, 5, 4, 4, 4, 5, 4, 4, 5,
                  5, 5, 5, 5, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4,
                  4, 4, 4, 3, 4, 3, 4, 3, 1, 5, 3, 3, 5, 3, 4, 4, 3, 3, 3, 3, 4, 3,
                  4, 4, 4, 4, 3, 4, 3, 3, 3, 4, 5, 3, 4, 3, 4, 5, 5, 5, 5, 5, 5, 4,
                  4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 4, 4, 5, 4, 4, 4, 4, 4,
                  5, 5, 5, 4, 5, 4, 4, 5, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 3, 3, 2,
                  3, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 5, 5, 5, 4, 5, 5, 4, 4, 4,
                  4, 5, 4, 5, 4, 3, 4, 5, 5, 4, 3, 3, 4, 3, 4, 5, 5, 5, 5, 3, 3, 5,
                  2, 3, 3, 3, 3, 4, 4, 5, 4, 4, 4, 5, 5, 3, 4, 3, 3, 5, 3, 3, 5, 4,
                  3, 4, 3, 2, 2, 3, 5, 5, 3, 4, 3, 3, 3, 5, 5, 4, 3, 3, 5, 3, 3, 3,
                  3, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 3, 5, 4, 4, 4, 3, 5, 4, 4, 4, 4,
                  5, 5, 4, 4, 4, 4, 3, 2, 3, 4, 3, 4, 2, 4, 5, 3, 4, 4, 4, 4, 4, 2,
                  3, 1, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 4, 3, 2, 3, 3, 4, 3,
                  5, 3, 3, 3, 3, 4, 1, 4, 3, 2, 1, 4, 2, 2, 2, 1, 2, 3, 2, 3, 2, 2,
                  3, 1, 4, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 5, 1, 1, 2, 1, 2, 1,
                  2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1,
                  2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 4, 2,
                  1, 2, 3, 3, 4, 3, 3, 5, 4, 4, 4, 3, 4, 3, 5, 2, 4, 4, 4, 4, 4, 4,
                  4, 4, 2, 3, 3, 5, 3, 3, 3, 4, 3, 3, 3, 5, 3, 3, 4, 5, 5, 3, 5, 3,
                  2, 4, 4, 3, 3, 4, 3, 4, 5, 5, 3, 3, 4, 4, 5, 4]])
        • energy_error
          (chain, draw)
          float64
          0.02139 -0.02762 ... 0.01447
          array([[ 2.13884648e-02, -2.76219814e-02,  3.45938191e-01,
                   1.49101606e-01, -2.52619688e-01,  8.56604749e-03,
                  -2.42837145e-02, -1.07623267e-02,  1.06822109e-01,
                  -8.65450768e-02,  4.23087489e-02,  3.67988967e-02,
                  -1.98361439e-01,  3.87770995e-02, -6.91225866e-02,
                   7.98907682e-02, -5.02984547e-01, -4.33307267e-01,
                   1.91784712e+00,  2.05797723e-02,  1.55879268e-01,
                  -1.54087695e-02,  6.58677999e-02,  5.93453991e-02,
                   1.58934599e-01, -1.72732422e-01, -1.61026725e-02,
                  -5.76937766e-02, -5.59996662e-01,  4.84201575e-01,
                  -3.56611749e-02,  2.87955684e-01, -2.30804723e-01,
                  -7.19262218e-02,  1.10829319e-02,  4.78115942e-02,
                  -4.91586548e-02, -9.30542887e-03, -1.84693849e-01,
                   1.59837158e-01, -1.81526081e-01,  5.33390246e-02,
                  -3.69030885e-02, -6.98565111e-02, -1.08858850e-03,
                   1.59655357e-02,  2.17823971e-03, -1.56327619e-02,
                   2.23495920e-02, -8.69994795e-02,  3.31741447e-01,
                  -2.30447600e-02, -1.41517915e-01, -5.48583599e-01,
                  -2.35100086e-01,  5.75928218e-02, -5.39413335e-02,
                  -3.00375165e-03, -4.74549793e-02,  6.09472682e-02,
                  -1.62126848e-02, -1.33028312e-01,  7.92130643e-01,
                   1.84643678e-01, -1.62123299e-01, -1.01264629e-01,
                  -5.28754332e-02,  1.21989436e-01, -2.67633215e-02,
                   3.88539993e-02,  3.28824790e-02,  2.54936255e-02,
                  -1.81800766e-01, -3.67217266e-03, -6.04753711e-01,
                   2.84617877e-01, -1.72562860e-01,  9.71792507e-02,
                  -4.87557714e-02, -2.70080509e-01,  4.72104760e-02,
                   1.44160450e-01,  6.54696430e-01,  2.34486570e-02,
                   3.50122724e-02,  1.66229567e-02, -8.69390601e-02,
                  -9.48929367e-02,  5.19869572e-02, -1.26476363e-01,
                  -3.43167878e-02,  1.26630229e-01, -2.26724582e-02,
                   2.80959744e-02, -2.32308101e+00, -7.41882821e-02,
                  -8.73753027e-03,  5.79346320e-01,  2.84464656e-01,
                  -1.77922047e-02, -5.45103783e-03, -9.93238830e-02,
                  -2.28421035e-02, -2.34405140e-01, -8.59739680e-01,
                  -6.70743587e-02, -8.33280287e-02,  2.18723634e-01,
                   1.26507313e+00,  2.10459688e+00, -2.77263378e+00,
                  -1.80047274e-01,  2.62225585e-01, -1.76489816e+00,
                   0.00000000e+00,  0.00000000e+00,  1.78473775e-02,
                   3.01062857e-01, -3.23842361e-02,  4.06595966e-01,
                   8.54705611e-02,  4.84731172e-02, -7.75596000e-02,
                   4.95168486e-02, -7.85851230e-02, -4.10505335e-03,
                   7.97435768e-02,  8.81264324e-02, -4.86691262e-02,
                   1.06753004e-01, -2.07359960e-02, -3.76409133e-02,
                   1.32710557e-01,  3.93136321e-02, -3.57727563e-02,
                  -7.91908447e-01, -7.69884347e-01,  3.96095578e-01,
                  -8.23127777e-01, -3.47228928e-01, -1.07451229e-01,
                  -1.12697337e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  3.69839763e-01,
                  -6.04722307e-01,  0.00000000e+00,  0.00000000e+00,
                   5.87546307e-01, -1.97357870e-01,  0.00000000e+00,
                   0.00000000e+00,  2.76580246e+00,  1.45765118e+00,
                   1.07939402e-01,  4.49764061e-01, -2.08004406e-01,
                  -2.90478218e-02,  9.51417336e-03, -4.76117230e-02,
                  -4.07150643e-02,  6.25340498e-02, -5.53515614e-02,
                  -1.45174417e-02,  3.37547914e-01, -2.65093107e-02,
                   2.23851124e-01,  2.25352515e-02,  2.07854420e-02,
                  -2.40734148e-01, -2.53124633e-02, -3.50364730e-02,
                   1.45461875e-02, -5.69459945e-02, -6.15580435e-01,
                  -8.58581551e-02,  4.71413880e-02, -9.72357843e-02,
                  -8.18197441e-02,  9.00727955e-01, -9.34535869e-01,
                  -1.45316574e-01,  3.81676739e-01, -6.10677225e-01,
                   3.34758306e+00, -2.36475861e-01,  3.66404357e-02,
                   9.55869052e-02,  2.54420638e-01,  1.18319809e-02,
                   1.35674156e-02,  6.40180940e-02, -1.39427561e-02,
                   2.56289461e-01,  1.11613052e-01, -1.62395416e-01,
                   2.01583159e-01, -4.47958408e-02, -7.06877889e-02,
                   2.39752659e-01, -7.64523967e-03,  4.04996144e-03,
                   2.98635361e-02, -6.75271131e-02, -1.23671125e-01,
                   2.74104077e-01, -4.61204678e-02,  8.07959588e-02,
                  -1.43885601e-02,  1.38688722e-01,  1.06086421e-01,
                  -7.48458162e-02,  1.35814094e-01, -8.65396399e-02,
                  -1.44243959e-01, -1.90744714e-01,  8.86523699e-03,
                   9.64904720e-02,  1.30871860e+00, -3.61522612e-02,
                  -1.67670997e-01, -3.29137759e-01,  2.37632789e-01,
                   9.43751397e-02,  3.75722643e-04, -1.73494208e+00,
                  -1.99383098e-01,  0.00000000e+00, -1.83799570e-01,
                   2.00238405e-01, -7.09103131e-01, -7.28439712e-01,
                   5.65835390e-01,  1.20880407e-01, -1.78774876e-01,
                  -3.46538581e-01,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00, -7.56146470e-02, -2.60752699e-01,
                   0.00000000e+00,  3.16662734e+00,  0.00000000e+00,
                  -1.84549765e+00,  0.00000000e+00,  3.28966726e-02,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   5.83271130e-01, -1.86380715e-01,  4.89279862e-01,
                   3.52607167e-01,  2.61751732e-02,  3.09955097e-02,
                   8.98893357e-02, -2.83091339e-02,  9.61442855e-02,
                   4.15310065e-03,  1.42835622e-01,  2.70198951e-02,
                   1.75208581e-01, -1.72660842e-02, -2.30613175e-02,
                  -2.11303697e-02, -4.67669315e-02, -1.56704566e-01,
                   1.01253781e-01, -9.65072356e-02,  7.01259631e-02,
                  -1.51215968e+00,  4.79342776e-01, -2.20409700e-01,
                   1.73188336e-02,  3.88790409e-02, -2.57816607e-01,
                  -1.80147632e-01,  8.12721707e-02,  2.38027561e-01,
                  -1.08868255e-02,  2.53773685e-01,  1.28210132e-01,
                   1.53369751e-02, -2.98262855e-01,  6.30772655e-02,
                  -1.03662290e-01,  5.35859297e-02, -4.74281191e-01,
                  -8.86484400e-03, -2.82725026e-01, -1.06104490e+00,
                  -8.53052320e-01,  0.00000000e+00,  0.00000000e+00,
                   2.89034263e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  4.53341595e-01, -7.81463156e-02,
                   2.09501980e-02, -7.65359579e-02,  2.11539443e-01,
                  -3.84230698e-02, -9.55781581e-01,  1.47224280e+00,
                  -3.61351732e-01,  2.14440659e-01, -2.42516665e-01,
                  -1.16548595e-01, -4.00348356e-01,  2.28002751e-01,
                  -4.19813783e-01,  1.44849197e-01,  2.17705135e-01,
                   4.09916609e-02,  7.11329253e-02, -6.85156621e-02,
                   4.76001489e-02, -2.62210478e-02,  2.50377718e-02,
                   1.65211491e-02, -1.31979946e-02, -1.73640141e-01,
                  -6.19777656e-01, -1.95719397e-02, -5.11574309e-02,
                  -2.07924946e-01,  7.47436268e-01,  1.28046065e-03,
                   9.85051738e-02, -7.35586664e-02,  5.42057062e-02,
                  -1.38166508e-02,  1.01761186e-01,  9.48588670e-02,
                   4.02562565e-01, -6.69791180e-02, -7.81526474e-02,
                   7.35737914e-02, -4.40464554e-01,  4.35162281e-02,
                   1.03162127e-02, -6.23496466e-02,  3.50116092e-02,
                  -2.73552198e-03,  2.28714699e-02,  9.03219194e-01,
                  -1.64619421e-01, -3.06043046e-01, -9.66109442e-02,
                  -2.00236361e-02,  2.42331660e-01,  1.55154427e-02,
                  -6.01366098e-01, -1.22046450e+00,  1.71453172e-02,
                  -1.08134679e-01,  6.31862496e-01, -1.67821656e-01,
                  -2.58968288e-02, -5.67036407e-01,  0.00000000e+00,
                   9.62348252e-01,  8.54211878e-02,  1.09683070e-01,
                   3.19565120e-01,  1.48491855e-01, -3.38324333e-02,
                   8.77650160e-02, -5.17177335e-03,  5.09910853e-02,
                  -2.53688735e-02, -1.08021960e-01,  1.75759671e-02,
                   3.20938754e-01,  2.98328680e-02,  1.19552219e-01,
                  -2.37394785e-01,  7.10934690e-02, -3.36213565e-02,
                  -5.55281232e-02,  3.32904475e-02, -3.62054862e-01,
                  -2.07025111e-01,  5.70884414e-02,  1.23568678e-01,
                   1.18134164e-01,  9.66051817e-03,  2.67759070e-02,
                  -8.31242308e-02, -8.50133661e-01, -2.88764962e-02,
                   1.38546815e+00,  2.09636667e-02, -3.21818586e-02,
                   1.97362666e-01, -1.71723184e+00,  9.43323910e-01,
                   0.00000000e+00, -6.98963943e-01,  2.09523960e-01,
                   8.03933453e-01, -1.60592909e-01,  7.27022730e-02,
                  -2.07549329e-01, -1.64422672e-01, -6.84155608e-03,
                   1.24596184e-01,  3.08387428e-01, -2.52145459e-01,
                   8.42469010e-02, -4.35565352e-02,  1.24873348e-01,
                  -2.14472682e-02, -3.53385057e-02, -1.55186745e-02,
                  -4.81239993e-04,  2.12244098e-02, -1.78673067e-02,
                   3.96281938e-03,  1.36273432e-01,  1.92865117e-02,
                   9.54081805e-02,  6.53824780e-03,  1.04864023e-01,
                  -6.89926849e-02,  8.57944941e-02, -3.58159664e-03,
                   9.14030295e-03,  1.44078803e-01, -6.95234968e-02,
                   1.40212407e-02, -5.51246367e-02,  1.85975532e-02,
                   1.78326556e-02,  1.40242376e-01,  9.75346894e-03,
                   1.17233486e-02,  8.88295760e-03, -9.16633834e-02,
                   1.73723086e-03, -7.51785173e-02, -1.51133197e-01,
                   1.68159521e-02, -1.24998947e-01, -3.82473715e-01,
                  -4.98435490e-01, -1.61895688e-01, -1.95764421e+00,
                   7.43982470e-01,  8.72158611e-02, -1.79381393e-02,
                  -6.59093590e-03, -5.99188472e-02,  4.64863932e-01,
                  -4.29402897e-01,  2.60659691e-01,  2.84278596e-01,
                   2.96400134e-02,  1.39114406e-01, -2.00778441e-01,
                   4.85677353e-03,  1.99758543e-01, -1.92278456e-01,
                  -1.19886478e-01, -2.46713802e-02, -4.06746115e-01,
                   1.44084837e-01, -1.21127523e-01,  1.31495182e-01,
                   2.43537028e-02, -4.52261938e-03,  2.78393304e-01,
                  -2.20276867e-01, -4.11923088e-02, -1.29095594e-01,
                   1.92659930e-02,  4.81357628e-02, -2.94026932e-02,
                  -1.83239927e-02, -9.48422411e-02,  5.38409379e-02,
                  -2.17251731e-05,  3.86147022e-02, -1.80618914e-01,
                   1.08824100e-01, -4.70831312e-01,  6.43243836e-01,
                   9.60106961e-02, -5.65732195e-02, -1.27889607e+00,
                   0.00000000e+00,  1.30370667e+00],
                 [ 5.29867604e-02,  1.08357049e+00,  0.00000000e+00,
                   0.00000000e+00, -7.91783611e-01, -6.98527960e-01,
                   2.68117610e-01,  2.76559442e+00,  4.69760378e-01,
                  -6.61369100e-02,  6.71052804e-01,  6.66919482e-02,
                  -1.13870065e-01,  4.58951815e-02, -3.95993915e-02,
                   6.45736925e-02, -6.34474819e-02, -2.56404519e-02,
                   1.55404743e-01,  1.45982098e-03,  1.90594261e-02,
                   6.88667455e-03,  9.90729645e-02, -1.14554540e-01,
                  -2.13156093e-02, -2.61531849e-02,  1.10938934e-01,
                  -4.46591531e-03, -2.28735394e-01,  1.63877727e-02,
                   1.36037589e-02, -1.98869804e-01,  3.64494618e-01,
                   7.59989756e-02, -1.11002241e-01, -1.48840354e-03,
                  -1.70932007e-01, -5.62505397e-01,  1.79578742e-01,
                  -1.02179943e+00, -7.02388712e-01,  4.02193461e-01,
                  -1.78783956e-01,  1.28016962e-01,  8.30440871e-02,
                   2.46844989e-01, -3.51407736e-02,  8.78477744e-02,
                   7.96021593e-02, -5.36636282e-02,  2.23356368e-02,
                  -1.18755061e-01,  4.15180045e-03,  1.07569064e-01,
                   1.31196600e-02,  1.42356123e-02,  3.21945203e-01,
                  -7.02696500e-01, -6.88247546e-02, -1.84827077e-01,
                   1.71063602e-01,  2.42948348e-02,  1.26302120e-01,
                  -4.17026613e-03,  1.99181269e-02, -1.42255436e-01,
                  -1.90494508e-01, -1.30836793e-01, -9.05617450e-02,
                   1.53301087e-01, -4.24007927e-02,  2.33249951e-01,
                   3.27890803e-02,  1.37279612e-01, -1.54533578e-02,
                   1.74095892e-01,  3.18055534e-02, -2.18859862e-01,
                   2.13545346e-01, -2.53994935e-01,  2.15043941e-02,
                   7.02416022e-03, -9.57145785e-03,  4.39451743e-02,
                   1.76778687e-02, -6.49947692e-03,  9.90645434e-03,
                  -1.62521157e-02, -7.81967982e-02,  1.51292227e-03,
                   1.27406113e-01, -9.92967279e-02, -1.23843840e+00,
                  -7.15563854e-02, -1.78355436e-02, -2.18804235e-01,
                   2.51098905e-01,  6.42577538e-03,  3.10938298e-02,
                  -4.52331151e-02,  4.98945075e-03,  1.76183702e-01,
                   8.64468893e-01, -1.51458810e-02,  2.13255655e-01,
                  -2.05060065e-01,  3.14563398e-02, -1.65088611e-01,
                  -5.67726814e-01,  6.92098943e-03, -1.39755373e-01,
                   4.31942974e-02, -1.99390985e-02,  7.76768935e-02,
                  -4.41846730e-01,  8.16421812e-02,  2.04133511e-01,
                  -1.70751598e-01,  0.00000000e+00, -2.80947885e-01,
                   3.29750302e-02, -7.22000191e-02,  5.00551588e-01,
                  -1.81316214e-01, -2.07505220e-01,  7.32237698e-02,
                   2.96529138e-01, -2.68064946e-01,  2.82732812e-01,
                  -5.08539053e-01, -1.61540389e-01, -2.68244557e-01,
                   1.39046501e-01, -8.89891947e-02,  6.72032724e-02,
                  -9.78763531e-02,  3.97494862e-02,  1.54862644e-01,
                  -5.37789896e-02, -1.55224999e+00, -3.95185328e-01,
                   2.12888868e-01,  3.33273040e-02,  9.62962465e-01,
                  -6.86973399e-01, -2.62444750e-01,  1.02196832e-01,
                  -7.12584119e-03,  4.25764271e-02,  1.13412891e-01,
                  -1.25505693e-01, -1.36565188e-02, -4.22194289e-02,
                   1.02912568e-01, -2.23807364e-02, -8.10436113e-02,
                  -4.33339234e-02,  5.84264578e-03, -9.06861205e-02,
                  -3.03362087e-01,  1.82713323e-01,  6.23392848e-02,
                  -1.27147349e-02, -4.32477681e-02,  1.23105924e+00,
                   3.93963960e-03, -4.13313155e-01,  3.16097122e-01,
                   9.27191972e-02,  6.88898115e-01, -1.48820814e-02,
                   9.72642658e-03,  5.41237005e-05,  2.12813293e-02,
                   4.00691386e-02, -2.67743747e-03, -6.72875479e-02,
                  -1.11757416e-01, -4.02988666e-02, -7.63948177e-03,
                  -1.45232894e-01, -1.33328792e-02,  1.96311918e-03,
                  -2.24161557e-03,  1.65641385e-02, -1.04919581e-01,
                   9.16628806e-03,  5.39553513e-02, -2.81245723e-02,
                  -2.47489402e-02,  4.97834198e-03,  1.85371821e-03,
                  -2.83772364e-02, -5.58649673e-02, -3.49812798e-01,
                  -7.76478750e-01,  0.00000000e+00,  3.09706959e-01,
                   0.00000000e+00,  6.47486581e-01,  6.60213815e-01,
                   2.45028868e-02, -5.01589211e-01,  5.32279017e-01,
                   1.94749929e-02,  3.88498360e-02,  1.09806416e-02,
                  -1.13105532e-01, -1.96225590e-04, -4.87980262e-02,
                   9.33403333e-02,  1.12765072e-01,  9.70837321e-03,
                  -2.64357208e-02,  5.06258514e-02,  1.85335788e-02,
                   2.27548431e-01, -3.10108685e-01,  3.39750059e-02,
                  -5.37747537e-02,  6.28811731e-02,  6.65074693e-03,
                  -3.28484782e-02,  9.66133878e-02, -1.60769436e-01,
                  -9.92295367e-02,  2.60132518e-01,  1.07706972e-02,
                   9.86376106e-02, -3.09420741e-01, -1.00443704e-02,
                  -4.72447242e-01,  1.84997962e-01,  8.47925456e-02,
                   1.13194798e-01, -2.89247194e-02, -9.78351211e-04,
                   2.77627593e-03, -1.60273870e-02,  1.14812646e-01,
                  -1.34408788e+00,  0.00000000e+00,  0.00000000e+00,
                   5.09827141e-01,  4.02428269e-03,  1.13854342e-01,
                   9.92114197e-02,  6.50489401e-02,  2.44551358e-01,
                   1.51702250e-01,  5.24461309e-01, -2.36194465e-02,
                  -6.46905244e-02,  1.50296933e-01, -4.36750468e-01,
                  -1.20388240e+00,  7.95160206e-01, -1.35665877e-02,
                  -3.30020288e-01,  8.72703950e-01, -3.28260378e-01,
                  -4.49765032e-01,  1.41498935e+00, -3.32277834e-02,
                   9.90441960e-02, -5.97136890e-02,  7.58358685e-01,
                  -4.56943643e-02,  0.00000000e+00,  5.50219457e-01,
                   1.05692977e-01,  1.04199859e-01, -1.25913122e-01,
                  -6.90288310e-02,  7.66803616e-03,  3.91761685e-02,
                   5.08517214e-01,  6.54204803e-02,  1.95139921e-02,
                   3.90507009e-02,  4.54045078e-02,  1.28687094e-01,
                  -2.60666929e-01,  2.21092967e-01,  7.88599446e-01,
                   2.99691605e-01,  3.26778070e-01,  2.22472765e-01,
                   2.03170877e-02, -2.76353477e-02, -8.28551180e-02,
                   1.77728382e-02,  7.90997652e-02, -6.12078190e-02,
                  -4.55222214e-02, -5.29234487e-03,  1.31253665e-01,
                  -2.66848763e-02, -1.50381766e-01,  1.41117824e-01,
                  -9.54720997e-01, -1.66692074e-01,  6.05963708e-02,
                  -1.64448381e-01,  1.88453394e-01,  2.79800354e-02,
                  -1.36515265e-01,  4.27172563e-03,  2.78791492e-03,
                  -1.42462528e-02,  1.11341096e-01, -4.72164188e-03,
                  -6.40281900e-02,  3.53410920e-02, -4.09742304e-02,
                   0.00000000e+00,  1.34899198e-01,  9.88243459e-02,
                   3.61316878e-02, -1.16109112e-02, -1.08567222e-01,
                   1.02271735e-01, -7.62946548e-02,  6.03946906e-02,
                  -1.02973700e-01,  7.33555972e-02, -4.17826845e-01,
                  -1.04926117e-01, -1.24626789e+00,  0.00000000e+00,
                  -2.52405059e+00,  0.00000000e+00,  0.00000000e+00,
                  -1.87099124e-02,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  6.46880273e-01,  0.00000000e+00,
                   3.52807793e-01,  4.15691179e-01,  4.14425030e-01,
                  -1.04216583e+00,  4.83810120e-01, -9.06242713e-01,
                   2.12490297e-01,  1.19756516e-01, -6.26708197e-01,
                   9.13219769e-01,  1.22333360e-01, -9.62359058e-02,
                   1.73853730e-03, -9.08990921e-01,  4.60430123e-01,
                  -7.04252042e-01,  1.17520015e-02, -3.39884475e-01,
                  -7.54149609e-01,  0.00000000e+00,  2.03053444e-01,
                   0.00000000e+00, -1.14124013e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00, -4.10244436e-01,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00, -6.59434631e-01,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  0.00000000e+00,  0.00000000e+00,
                   0.00000000e+00,  8.05219901e-01,  0.00000000e+00,
                   0.00000000e+00,  3.32375790e+00, -1.50841567e+00,
                   1.86938128e+00,  8.16895081e-01,  5.29559878e-01,
                   5.19292210e-01, -8.13311185e-02,  8.02468886e-02,
                  -5.63908587e-02,  2.14739622e-01, -7.06010109e-01,
                   4.43969901e-01, -2.34210134e-01, -1.05802315e-01,
                   1.15661181e-01,  5.81235322e-02, -1.62405644e-01,
                   2.37889803e-02,  8.25684300e-02, -2.51293792e-01,
                  -9.89725572e-02, -1.73632877e-01, -2.76698598e-01,
                   6.67768861e-01, -1.09710542e+00, -7.47905224e-01,
                   8.80749701e-02,  3.84732468e-01, -5.99409722e-01,
                  -6.93561382e-02, -1.91380168e-02,  1.39509626e+00,
                  -3.67732537e-01,  2.52806021e-03, -8.91880410e-01,
                  -1.36342821e+00,  3.11100278e-01, -2.42921254e-02,
                  -3.59466669e-01,  2.73348266e-01, -1.24154421e-01,
                   8.08635775e-02, -1.27439015e-01,  7.97016597e-01,
                   2.87387080e-02, -1.55893303e-01, -5.17823776e-02,
                  -1.23034475e-01, -7.26487279e-02,  8.76958332e-02,
                  -1.09581125e-02, -3.07102422e-02,  6.18450437e-02,
                   1.65230466e-01,  1.97165881e-02, -3.73063757e-02,
                  -3.70917408e-02,  1.44712320e-02]])
      • created_at :
        2020-06-10T17:34:00.071123
        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
        • school: 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])
        • school
          (school)
          <U16
          'Choate' ... 'Mt. Hermon'
          array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
                 'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype='<U16')
        • theta
          (chain, draw, school)
          float64
          -5.382 -1.8 ... 15.41 -0.6966
          array([[[-5.38226531e+00, -1.79958337e+00, -9.71167365e-02, ...,
                   -3.54731587e+00, -2.96291254e+00,  5.01614415e-02],
                  [-1.74895087e+00, -3.73529936e+00, -2.89356820e+00, ...,
                    6.21177591e-01,  1.19220705e+00, -5.91065699e+00],
                  [ 1.36107067e+02, -6.29995712e+01, -1.29488317e+01, ...,
                    8.71188666e+01,  1.24962205e+02,  1.05190182e+02],
                  ...,
                  [-9.20105057e+00, -8.95828682e+00,  2.13497986e+00, ...,
                    8.85972725e-01,  4.63084069e+00, -1.49099388e+00],
                  [-1.41632386e+01, -1.47380531e+01, -1.43516071e+01, ...,
                   -1.35300300e+01, -1.40524229e+01, -1.41346425e+01],
                  [ 2.47851881e+00,  3.74327972e+01,  3.74364109e+01, ...,
                   -2.95931232e+01,  1.54051753e+01, -6.96646866e-01]]])
        • tau_log__
          (chain, draw)
          float64
          0.528 0.646 4.446 ... 0.3069 3.251
          array([[ 0.52802804,  0.64603241,  4.44591589,  2.03771347,  2.2004995 ,
                   1.92665312,  1.16657263,  1.93375145, -0.61434131,  1.14662839,
                   1.26944222,  1.08537899,  3.07748239,  1.55287501,  3.3765186 ,
                   2.22789734,  2.43660779,  0.85368965,  1.84587953,  1.12354145,
                   0.87632413, -0.82353771,  1.422862  , -0.27214488,  0.95058845,
                   1.69094221,  0.64387814,  1.11963136,  1.56115371,  1.88093363,
                  -3.68495256,  4.20646463,  1.39855138,  0.15627904,  1.93707072,
                   3.06379112,  3.94807645,  1.82564146,  3.16197141,  1.68305607,
                   0.86171504,  1.56482235, -1.41840816,  2.83993707,  0.44851719,
                   3.5153974 ,  2.9869387 ,  0.66312043,  0.63840389,  2.54128679,
                   3.10152016,  4.4014825 ,  4.66087266,  2.09588866,  0.2216517 ,
                   3.11450009,  1.93419224,  3.18878472,  0.97568785,  1.92525151,
                   1.33898909,  2.44830283,  0.74075717,  2.22883782,  0.9511615 ,
                   0.54962973,  2.32959659,  3.22355548,  2.4782994 ,  1.30215297,
                   1.51849574,  1.02643235,  3.90508783,  2.43905148,  1.31065166,
                   0.86832013,  0.89095035,  0.84036308, -0.8297316 ,  1.73389108,
                   1.5693849 , -0.11027874,  3.25566037,  0.87331244,  1.89402072,
                   7.674472  ,  2.14377257,  2.52063138,  3.53039869, -0.59016266,
                  -1.0600327 ,  0.87960494,  5.04429127,  3.19938272,  1.36062139,
                   0.96180598, -2.12838769,  0.92437329,  0.28042094,  3.56313283,
                   1.07773096,  1.53210145,  1.22998814,  1.10580605,  3.03064638,
                   0.76628593,  1.80771578,  0.29673895,  3.01430466,  0.99770597,
                   3.1323281 ,  2.49731516, -2.15107938,  2.28196402,  2.89990267,
                   1.51188188,  1.95027935, -0.90883014,  3.29461717,  1.495148  ,
                   0.69033899,  1.90869467, -1.01673998,  3.30479678,  2.4123436 ,
                   0.76196697,  0.5185042 ,  1.24869888,  1.52338784,  4.26068941,
                  -0.03473632,  2.21950376,  0.50826182, -0.89439556,  2.02416213,
                   5.02064112,  2.77193971,  2.97659281, -0.52000919,  3.44674674,
                   2.00261986,  2.82799101,  1.06314865,  1.80267687,  2.3456437 ,
                  -0.31984801,  3.23621612,  2.73862399,  2.73330405,  0.52398821,
                  -0.47543239,  2.19536564,  2.76669784,  6.90485173,  1.98476661,
                  -0.82092589,  1.70852183,  2.07933642,  3.98550116,  2.20570672,
                   1.85343692,  2.71408238,  3.74893398, -0.63555569,  1.94890547,
                   4.27596559,  3.06782652,  2.16728136,  4.53995315,  3.62074141,
                   2.73172331,  1.95764257, -0.07057574, -0.06659884,  1.22412566,
                   0.79900457,  1.77737782,  1.54449579,  1.10369077,  2.41906546,
                   1.41722192,  1.88967531, -0.83556836,  1.07597554, -0.37563568,
                   2.34259707,  1.6252503 ,  3.60433022,  0.35791251, -0.1425261 ,
                   2.14160481,  1.7165216 ,  0.88010215,  0.97934447,  1.52456834,
                   0.53721242,  0.98818555,  1.49064049,  1.88019418, -0.07847492,
                   0.35097773,  2.54557015,  4.88699387,  1.28286152,  0.70738085,
                   3.4769718 ,  0.81668544,  0.6363184 ,  2.32885573,  3.29646478,
                   0.76462255,  1.30429672,  1.07312271,  0.31803258,  4.38300279,
                   1.47931718,  0.28835533,  1.49624369,  0.89031284,  4.19695513,
                   0.52949698, -0.52047844,  0.13686976,  1.26311853,  1.64056743,
                   1.66053764,  1.7382547 , -0.41750605,  2.8284805 , -0.04736669,
                  -1.16845067,  1.12478661,  0.77820123,  2.24236   ,  0.98515536,
                   0.95314444,  1.18091876,  0.38676273,  3.38754312,  1.85234807,
                   0.96258862,  4.54561389,  3.56223943,  1.40141289,  2.39554979,
                   1.27167264,  3.70972877,  2.13233021,  2.04852201,  0.93888247,
                   2.29813154, -0.4218184 ,  4.31554429, -0.75979545,  1.41339356,
                   3.23231714,  2.24009664,  1.17023819,  3.14013099,  3.01107118,
                   1.21830941, -2.08073048,  2.37993757,  2.25519001,  1.24619295,
                   1.93124087,  1.86519598,  2.71098661,  2.80225801,  2.29881517,
                   3.81877997,  1.90476785,  2.21620119, -1.17048021,  2.0518102 ,
                   3.32649472,  1.51980144, -0.22356815,  1.81837874,  1.68757113,
                   0.99288112,  2.81379214,  1.56501761,  2.00666217,  2.03159021,
                   1.43245518,  2.66322041,  0.93642038,  2.81271743,  2.34473144,
                  -0.03455206,  3.01590837,  0.23110034,  0.38012704,  3.53961697,
                   3.73942706,  1.16713373,  2.254044  ,  3.03439196,  2.05163818,
                   0.28187247,  1.31883302, -0.12841473,  0.04041703,  3.10367754,
                   1.12410732,  1.10593433,  0.1894269 ,  0.95628139,  1.50375704,
                   3.00445703,  1.99377088,  2.87753714,  0.65867184,  1.98279826,
                   0.27003725,  1.47657283,  1.33263893,  1.33469376,  2.80257001,
                   1.70782907,  1.61365799,  2.52340063,  0.76098985,  3.08917828,
                   3.07552012,  2.43713442,  0.30149493,  0.94484852,  0.08348638,
                   1.36779746,  2.19406207, -0.134692  ,  1.30831115, -0.58514878,
                   3.34836235,  2.76211038,  3.62256876,  0.926042  ,  2.95076046,
                   3.04568129,  2.29751952,  3.7560286 , -0.52621514, -1.39125821,
                   1.55624365,  0.11221508,  1.60862802,  1.73693892,  2.55578278,
                   1.21870975,  1.22264216,  0.28720504, -2.60721455,  1.98171587,
                   2.87771508,  1.68650907,  0.15731541,  2.83036269, -1.79132602,
                   0.20021825,  1.91254625,  2.07783201, -1.51867876,  4.03209921,
                   2.53331348,  0.46678346,  1.09793542,  4.72351363,  1.89102585,
                   1.56937321,  0.99687841,  2.46763289,  0.41399182,  1.9467013 ,
                   0.35699392,  3.16951951,  2.02572836,  2.24290485,  2.9442996 ,
                   1.90985889,  1.00927195, -0.37086168,  2.72358631,  2.07719728,
                  -1.19256848,  3.06111124,  1.66074204, -0.24131961,  0.66943485,
                   4.14147793, -0.48182715,  1.07773209,  0.87589479, -0.20432774,
                   1.84583944,  3.22984921,  1.55093341,  0.76935547,  0.84383461,
                   2.5921779 ,  4.90013393,  2.27734914,  2.321011  ,  2.55360359,
                   1.57008105,  1.92815241,  1.65699237,  1.87994199,  0.88749961,
                   3.46886987,  1.55421117,  0.77227048,  0.34474624,  3.1385769 ,
                   1.84170822,  1.45482108,  1.91309616,  0.62334794,  2.88330701,
                   2.77021071,  1.74828659,  2.5945097 ,  2.05027469,  2.05739267,
                   1.79843166,  2.80401809,  4.23733813,  1.59335886,  0.89887479,
                   2.79427037,  1.58325087,  1.09113867,  0.36239403, -1.4032523 ,
                   2.24263335, -1.31325467,  1.91793298,  4.81581366,  0.92220502,
                   0.36412751,  2.00470092,  0.4144842 ,  2.10516808,  0.99151169,
                   2.81961449,  1.99016591,  1.65644462,  2.05856512,  2.25347137,
                  -1.21480834,  2.0536771 ,  1.40843489,  2.20339534,  1.07278613,
                   2.12874324,  0.60039108,  4.36005154,  1.07917998,  0.14059304,
                   4.33771053,  0.04721516,  2.46570619,  1.82797735,  1.4638865 ,
                   3.67632633,  0.81256843,  0.68408822,  1.28039945,  2.17307181,
                   1.66016273,  4.02903614,  3.4233466 ,  1.91198079,  1.70573402,
                   2.71329587,  3.30306289,  3.01543452, -0.51149176,  1.23456667,
                   2.23567751,  1.76779912,  0.97030476,  0.19631047,  0.04722606,
                   1.74783445,  6.54852844, -0.24548393,  1.57168587,  4.37560667,
                   2.53213115,  2.44066218,  0.15702267,  2.85077673,  1.95909271,
                   0.84070148,  1.63576738,  1.37276902,  0.3069483 ,  3.25133764]])
        • tau
          (chain, draw)
          float64
          1.696 1.908 85.28 ... 1.359 25.82
          array([[1.69558538e+00, 1.90795581e+00, 8.52779474e+01, 7.67304451e+00,
                  9.02952258e+00, 6.86649042e+00, 3.21096859e+00, 6.91540445e+00,
                  5.40997126e-01, 3.14756264e+00, 3.55886693e+00, 2.96056162e+00,
                  2.17036922e+01, 4.72503520e+00, 2.92686976e+01, 9.28033219e+00,
                  1.14341877e+01, 2.34829526e+00, 6.33366799e+00, 3.07572747e+00,
                  2.40205381e+00, 4.38876289e-01, 4.14897783e+00, 7.61743894e-01,
                  2.58723166e+00, 5.42458938e+00, 1.90384998e+00, 3.06372458e+00,
                  4.76431471e+00, 6.55962625e+00, 2.50983655e-02, 6.71188301e+01,
                  4.04932979e+00, 1.16915240e+00, 6.93839665e+00, 2.14085659e+01,
                  5.18355625e+01, 6.20677511e+00, 2.36171090e+01, 5.38197855e+00,
                  2.36721708e+00, 4.78182535e+00, 2.42099092e-01, 1.71146884e+01,
                  1.56598841e+00, 3.36292894e+01, 1.98248996e+01, 1.94083915e+00,
                  1.89345630e+00, 1.26959976e+01, 2.22317214e+01, 8.15717088e+01,
                  1.05728306e+02, 8.13266492e+00, 1.24813658e+00, 2.25221684e+01,
                  6.91845337e+00, 2.42589280e+01, 2.65299143e+00, 6.85687305e+00,
                  3.81518474e+00, 1.15686960e+01, 2.09752310e+00, 9.28906428e+00,
                  2.58871471e+00, 1.73261136e+00, 1.02737962e+01, 2.51172655e+01,
                  1.19209743e+01, 3.67720505e+00, 4.56535257e+00, 2.79109041e+00,
                  4.96544408e+01, 1.14621635e+01, 3.70858966e+00, 2.38290452e+00,
                  2.43744499e+00, 2.31720816e+00, 4.36166339e-01, 5.66264492e+00,
                  4.80369252e+00, 8.95584469e-01, 2.59367368e+01, 2.39483045e+00,
                  6.64603686e+00, 2.15268677e+03, 8.53156288e+00, 1.24364463e+01,
                  3.41375751e+01, 5.54237127e-01, 3.46444480e-01, 2.40994744e+00,
                  1.55134311e+02, 2.45173913e+01, 3.89861510e+00, 2.61641740e+00,
                  1.19029051e-01, 2.52028828e+00, 1.32368689e+00, 3.52735302e+01,
                  2.93800552e+00, 4.62789192e+00, 3.42118897e+00, 3.02165908e+00,
                  2.07106152e+01, 2.15175960e+00, 6.09650578e+00, 1.34546402e+00,
                  2.03749185e+01, 2.71205316e+00, 2.29272945e+01, 1.21498298e+01,
                  1.16358495e-01, 9.79590083e+00, 1.81723766e+01, 4.53525758e+00,
                  7.03065133e+00, 4.02995395e-01, 2.69670882e+01, 4.45999657e+00,
                  1.99439149e+00, 6.74427954e+00, 3.61772406e-01, 2.72430047e+01,
                  1.11600853e+01, 2.14248629e+00, 1.67951355e+00, 3.48580454e+00,
                  4.58774145e+00, 7.08588173e+01, 9.65860065e-01, 9.20276298e+00,
                  1.66239914e+00, 4.08854652e-01, 7.56976577e+00, 1.51508408e+02,
                  1.59896191e+01, 1.96208506e+01, 5.94515084e-01, 3.13980798e+01,
                  7.40843975e+00, 1.69114518e+01, 2.89547349e+00, 6.06586327e+00,
                  1.04399908e+01, 7.26259414e-01, 2.54372879e+01, 1.54656896e+01,
                  1.53836314e+01, 1.68874933e+00, 6.21616220e-01, 8.98328511e+00,
                  1.59060229e+01, 9.97100663e+02, 7.27734876e+00, 4.40024050e-01,
                  5.52079476e+00, 7.99915905e+00, 5.38122515e+01, 9.07666399e+00,
                  6.38171530e+00, 1.50907561e+01, 4.24757780e+01, 5.29641090e-01,
                  7.02099865e+00, 7.19495799e+01, 2.14951327e+01, 8.73450574e+00,
                  9.36864108e+01, 3.73652607e+01, 1.53593331e+01, 7.08261060e+00,
                  9.31857159e-01, 9.35570439e-01, 3.40119100e+00, 2.22332665e+00,
                  5.91432763e+00, 4.68560849e+00, 3.01527419e+00, 1.12353546e+01,
                  4.12564315e+00, 6.61721982e+00, 4.33627956e-01, 2.93285262e+00,
                  6.86852520e-01, 1.04082324e+01, 5.07969033e+00, 3.67570567e+01,
                  1.43034047e+00, 8.67164925e-01, 8.51308853e+00, 5.56513700e+00,
                  2.41114600e+00, 2.66271019e+00, 4.59316047e+00, 1.71123001e+00,
                  2.68635578e+00, 4.43993834e+00, 6.55477757e+00, 9.24525243e-01,
                  1.42045569e+00, 1.27504957e+01, 1.32554499e+02, 3.60694632e+00,
                  2.02867091e+00, 3.23615761e+01, 2.26298658e+00, 1.88951163e+00,
                  1.02661876e+01, 2.70169590e+01, 2.14818339e+00, 3.68509653e+00,
                  2.92449761e+00, 1.37442104e+00, 8.00781308e+01, 4.38994713e+00,
                  1.33423132e+00, 4.46488604e+00, 2.43589159e+00, 6.64835883e+01,
                  1.69807793e+00, 5.94236176e-01, 1.14667879e+00, 3.53643278e+00,
                  5.15809552e+00, 5.26213923e+00, 5.68740855e+00, 6.58687507e-01,
                  1.69197317e+01, 9.53737609e-01, 3.10848174e-01, 3.07955965e+00,
                  2.17755183e+00, 9.41552572e+00, 2.67822793e+00, 2.59385305e+00,
                  3.25736556e+00, 1.47220714e+00, 2.95931561e+01, 6.37477036e+00,
                  2.61846592e+00, 9.42182495e+01, 3.52420308e+01, 4.06093356e+00,
                  1.09742299e+01, 3.56681357e+00, 4.08427274e+01, 8.43449809e+00,
                  7.75642870e+00, 2.55712216e+00, 9.95556346e+00, 6.55853129e-01,
                  7.48543547e+01, 4.67762097e-01, 4.10987887e+00, 2.53383014e+01,
                  9.39423913e+00, 3.22276019e+00, 2.31068935e+01, 2.03091430e+01,
                  3.38146621e+00, 1.24838987e-01, 1.08042284e+01, 9.53710531e+00,
                  3.47708031e+00, 6.89806454e+00, 6.45720126e+00, 1.50441108e+01,
                  1.64818209e+01, 9.96237177e+00, 4.55486040e+01, 6.71784787e+00,
                  9.17242029e+00, 3.10217936e-01, 7.78197527e+00, 2.78405816e+01,
                  4.57131744e+00, 7.99660390e-01, 6.16186037e+00, 5.40633346e+00,
                  2.69899943e+00, 1.66730249e+01, 4.78275916e+00, 7.43844762e+00,
                  7.62620396e+00, 4.18897124e+00, 1.43424032e+01, 2.55083405e+00,
                  1.66551159e+01, 1.04304711e+01, 9.66038050e-01, 2.04076202e+01,
                  1.25998566e+00, 1.46247036e+00, 3.44537199e+01, 4.20738775e+01,
                  3.21277075e+00, 9.52618197e+00, 2.07883340e+01, 7.78063679e+00,
                  1.32560966e+00, 3.73905541e+00, 8.79488553e-01, 1.04124491e+00,
                  2.22797355e+01, 3.07746842e+00, 3.02204674e+00, 1.20855677e+00,
                  2.60200262e+00, 4.49855863e+00, 2.01752585e+01, 7.34317187e+00,
                  1.77704532e+01, 1.93222432e+00, 7.26303846e+00, 1.31001325e+00,
                  4.37791606e+00, 3.79103447e+00, 3.79883240e+00, 1.64869640e+01,
                  5.51697150e+00, 5.02114498e+00, 1.24709336e+01, 2.14039383e+00,
                  2.19590265e+01, 2.16611453e+01, 1.14402109e+01, 1.35187825e+00,
                  2.57242367e+00, 1.08707041e+00, 3.92669246e+00, 8.97158239e+00,
                  8.73985055e-01, 3.69991981e+00, 5.57022984e-01, 2.84560943e+01,
                  1.58332219e+01, 3.74336024e+01, 2.52449742e+00, 1.91204885e+01,
                  2.10243499e+01, 9.94947233e+00, 4.27781989e+01, 5.90836979e-01,
                  2.48762111e-01, 4.74097896e+00, 1.11875346e+00, 4.99595218e+00,
                  5.67993009e+00, 1.28813790e+01, 3.38282022e+00, 3.39614906e+00,
                  1.33269744e+00, 7.37396559e-02, 7.25518124e+00, 1.77736154e+01,
                  5.40059465e+00, 1.17036470e+00, 1.69516080e+01, 1.66738923e-01,
                  1.22166936e+00, 6.77030577e+00, 7.98713408e+00, 2.19001049e-01,
                  5.63791385e+01, 1.25951709e+01, 1.59485602e+00, 2.99797009e+00,
                  1.12563064e+02, 6.62616265e+00, 4.80363638e+00, 2.70980971e+00,
                  1.17944949e+01, 1.51284476e+00, 7.00554028e+00, 1.42902718e+00,
                  2.37960479e+01, 7.58163108e+00, 9.42065719e+00, 1.89973521e+01,
                  6.75213593e+00, 2.74360279e+00, 6.90139393e-01, 1.52348613e+01,
                  7.98206602e+00, 3.03440881e-01, 2.13512704e+01, 5.26321493e+00,
                  7.85590507e-01, 1.95313320e+00, 6.28957080e+01, 6.17653813e-01,
                  2.93800884e+00, 2.40102274e+00, 8.15195155e-01, 6.33341410e+00,
                  2.52758454e+01, 4.71586995e+00, 2.15837467e+00, 2.32526638e+00,
                  1.33588342e+01, 1.34307766e+02, 9.75079807e+00, 1.01859671e+01,
                  1.28533386e+01, 4.80703777e+00, 6.87679298e+00, 5.24351657e+00,
                  6.55312472e+00, 2.42904848e+00, 3.21004444e+01, 4.73135282e+00,
                  2.16467554e+00, 1.41163165e+00, 2.30710111e+01, 6.30730332e+00,
                  4.28371694e+00, 6.77402984e+00, 1.86516206e+00, 1.78732828e+01,
                  1.59619970e+01, 5.74475113e+00, 1.33900206e+01, 7.77003514e+00,
                  7.82553943e+00, 6.04016702e+00, 1.65108557e+01, 6.92233432e+01,
                  4.92024763e+00, 2.45683710e+00, 1.63506945e+01, 4.87076432e+00,
                  2.97766273e+00, 1.43676496e+00, 2.45796259e-01, 9.41809979e+00,
                  2.68943310e-01, 6.80687399e+00, 1.23447216e+02, 2.51482952e+00,
                  1.43925772e+00, 7.42387321e+00, 1.51358983e+00, 8.20848259e+00,
                  2.69530586e+00, 1.67703842e+01, 7.31674755e+00, 5.24064520e+00,
                  7.83471982e+00, 9.52072849e+00, 2.96766889e-01, 7.79651701e+00,
                  4.08954978e+00, 9.05570857e+00, 2.92351345e+00, 8.40429801e+00,
                  1.82283154e+00, 7.82611681e+01, 2.94226585e+00, 1.15095616e+00,
                  7.65321202e+01, 1.04834755e+00, 1.17717924e+01, 6.22129041e+00,
                  4.32272721e+00, 3.95010135e+01, 2.25368900e+00, 1.98196390e+00,
                  3.59807669e+00, 8.78522919e+00, 5.26016676e+00, 5.62067099e+01,
                  3.06718901e+01, 6.76647854e+00, 5.50542530e+00, 1.50788918e+01,
                  2.71958092e+01, 2.03979523e+01, 5.99600454e-01, 3.43688889e+00,
                  9.35281630e+00, 5.85794655e+00, 2.63874851e+00, 1.21690466e+00,
                  1.04835897e+00, 5.74215428e+00, 6.98215948e+02, 7.82325853e-01,
                  4.81475840e+00, 7.94880480e+01, 1.25802881e+01, 1.14806405e+01,
                  1.17002214e+00, 1.73012151e+01, 7.09288881e+00, 2.31799243e+00,
                  5.13339575e+00, 3.94626284e+00, 1.35927069e+00, 2.58248611e+01]])
        • mu
          (chain, draw)
          float64
          -2.269 -1.444 ... -13.85 2.351
          array([[-2.26914550e+00, -1.44379588e+00,  1.00247187e+00,
                   1.20384364e-01,  7.50899815e+00, -3.67857131e+00,
                  -3.41881414e+00,  9.00068394e-01,  4.74484082e+00,
                  -5.03946470e+00, -4.17515583e-01, -9.43139925e+00,
                  -7.78615651e+00,  1.37588155e+01,  1.14887933e+01,
                   2.37310628e+00,  4.32478351e+00, -1.10107632e+00,
                  -4.18776151e+00,  3.98082627e+00, -7.52501927e-02,
                   5.11533548e+00,  3.97637078e-01, -2.58538397e+00,
                   2.36566128e+00,  1.98314597e-01,  2.68998912e+00,
                   2.89991381e+00,  5.66045957e+00, -6.24108636e+00,
                  -2.93500369e+00,  3.24841216e+00,  1.06401298e+00,
                  -3.21620282e-01,  4.48282174e+00,  3.36763018e+00,
                  -7.28688484e+00,  3.19789919e+00, -1.02234401e+01,
                   5.66967753e+00, -3.82273554e-01,  1.57131978e+00,
                   1.62094295e-01,  6.11246869e+00, -5.06750759e+00,
                  -6.05770894e+00, -1.01217574e+00, -3.57922945e+00,
                  -1.42625824e-01, -3.88505130e+00, -1.11226605e-01,
                   1.49267405e+00,  3.19517489e+00, -1.41724096e+01,
                   8.93102254e+00, -6.79233656e+00, -2.97608190e+00,
                   6.53525494e+00,  7.32431288e+00, -6.22294184e-01,
                   4.22087794e+00, -7.17817189e+00,  7.18534060e+00,
                  -5.85916914e+00, -3.68658443e+00, -1.54499032e+00,
                  -5.91867788e+00,  2.41070761e+00, -1.82189655e-01,
                   1.00955171e+01, -1.68402574e-01,  4.79286819e+00,
                   4.16613720e-01,  5.94249080e+00, -7.40626372e+00,
                  -1.10091923e+00, -8.17046550e+00,  2.96828991e+00,
                   1.33609861e+00,  2.46604063e+00,  2.87990847e+00,
                   7.35880269e+00, -6.94166969e+00,  9.11007376e+00,
                  -3.23877385e+00,  5.36554937e+00,  1.15064689e+01,
                   5.76892301e+00,  5.51232338e+00, -7.65590672e+00,
                   3.61150388e+00, -7.78326963e+00, -1.02653144e+01,
                  -9.96393894e-01, -3.60386880e+00, -2.20290135e+00,
                  -5.70944366e+00,  3.83011464e+00,  6.01597897e+00,
                  -8.10235846e-01,  8.06381402e+00,  3.31047568e+00,
                  -2.60956318e+00,  1.08448452e+01, -1.24302467e+00,
                  -2.90057336e+00, -4.56554129e+00, -6.14255423e+00,
                  -1.71616440e+00, -2.05711995e-01,  6.85348929e+00,
                  -9.96713660e+00, -9.28799933e-01, -1.03358337e+00,
                   2.57186374e-01, -5.35563639e+00,  9.90086531e-01,
                  -8.67753211e+00,  4.09393361e+00,  3.66635132e+00,
                   1.10163161e+01, -1.57741572e+00, -8.56189891e+00,
                   5.21268899e+00,  1.09600101e+00, -3.74754443e+00,
                  -6.73344862e+00,  5.56081582e+00, -2.25182092e+00,
                  -2.30891416e+00, -8.87182355e+00,  7.20544220e+00,
                  -1.25258724e+00,  1.81740608e+00, -1.38340178e+00,
                   4.43151779e+00,  3.11364745e-01,  1.80431456e+00,
                   1.66160963e+00, -9.94841913e-01,  4.81862289e+00,
                  -3.57409200e+00, -3.20904470e+00,  6.34046078e+00,
                  -2.00449355e+00, -1.23050437e+00,  8.32507098e-01,
                  -3.09169124e+00,  5.78198599e+00,  4.21700741e+00,
                  -3.39655429e+00,  6.92700458e+00, -1.49165366e+00,
                   7.81107367e+00, -4.94483784e-01,  7.56923593e+00,
                  -5.30515012e+00, -5.85327919e+00, -3.50480070e+00,
                  -5.23692581e-02, -1.06624775e+00,  7.20441446e+00,
                  -3.54085457e-01,  8.29064002e-01,  1.39285564e+00,
                  -1.15704321e+00,  5.57577071e+00,  3.24710988e+00,
                   1.78594214e+00, -8.07672404e-01, -3.12079615e+00,
                  -6.39280950e+00, -2.11491058e+00,  6.40123671e+00,
                  -3.81990354e+00,  2.28507210e+00, -9.05782652e+00,
                  -4.13109571e+00,  8.87021352e-01, -1.88507149e+00,
                  -8.28541976e-01,  6.22856500e-01,  1.82066906e-01,
                  -3.61023759e+00,  1.14931246e+01, -1.23935807e+00,
                  -1.56700306e+00,  7.89523269e-01,  1.11502633e+01,
                  -3.57961405e+00,  6.16122117e+00, -6.21412080e+00,
                  -2.49911170e+00, -4.54631976e+00, -1.56224202e+00,
                  -4.00126291e-01, -3.77142624e+00, -5.22574118e-01,
                   6.04021511e+00,  2.88252810e+00,  4.27811829e-02,
                  -9.18043904e+00, -7.52477332e+00,  7.58841972e-01,
                  -1.08805160e+00, -6.37013658e+00,  3.56744543e+00,
                  -5.88553496e-01, -5.04499862e+00, -1.90237733e+00,
                   1.21063404e+00,  6.01739583e+00,  3.89519925e+00,
                   1.46063843e+01,  1.59599097e+00, -4.97931878e+00,
                  -5.87907076e+00,  1.72782286e+00,  1.01695155e+01,
                   7.71089561e+00, -4.36515986e+00,  7.28454898e-01,
                  -3.45599056e+00,  2.56623826e+00,  3.34807102e+00,
                  -4.22890950e+00, -6.68538154e+00, -7.18746053e+00,
                  -3.71949440e-01, -7.29425530e-01,  4.65003658e+00,
                   7.24108076e+00,  1.78500470e+00,  1.32963479e+00,
                  -2.56393403e+00, -5.47257096e+00, -8.16716359e+00,
                  -3.20658154e+00, -5.54567808e+00,  2.68144900e+00,
                  -9.44654046e-01,  6.22950703e+00,  5.33028846e+00,
                   6.30216377e+00,  1.45439681e+00,  8.49604293e-01,
                   4.60170232e-01, -1.08418117e+01, -5.87623852e+00,
                   2.50280700e+00, -2.45585154e+00,  3.62681771e-01,
                  -5.75586243e+00,  3.58214427e+00, -3.55950829e-01,
                   6.72812969e+00,  2.72842542e+00,  5.90017339e+00,
                  -5.37280575e-01,  2.46207329e+00,  8.32428945e+00,
                  -1.40517787e+00,  3.17291320e+00, -7.33923433e+00,
                   8.87922120e+00, -1.82098978e+01, -5.99871228e+00,
                  -6.12222522e+00, -1.15648303e+00, -4.63117527e+00,
                   8.72392558e+00, -4.65776509e+00, -2.07601816e+00,
                  -7.39749412e-01, -5.80720370e+00, -6.74127267e+00,
                  -3.75952249e-01,  8.94247941e+00, -2.56290509e+00,
                   3.78329020e+00,  2.27918175e+00, -5.43441254e+00,
                  -4.71026255e+00, -5.76979539e+00,  3.48927095e+00,
                  -6.99189227e-01,  1.65687012e+00,  1.46151619e+00,
                   5.97250928e+00, -5.04170154e+00,  1.11750322e+00,
                   4.76567073e+00, -2.96851333e+00,  4.54157643e+00,
                  -7.13957605e-01,  7.58938483e+00, -7.67721665e-01,
                  -4.95258618e+00, -1.01601101e+01, -4.73451448e+00,
                   2.37501451e+00,  8.96241563e+00, -2.22830040e+00,
                   4.10517688e+00,  5.12461896e+00, -3.12221739e+00,
                  -1.42471529e-02, -2.42206871e+00, -5.95638141e+00,
                   1.24113247e+00, -2.87754658e-01, -9.84387254e+00,
                   6.31501185e+00,  6.90396625e+00, -2.02165726e+00,
                  -3.20936389e+00, -8.59270599e-01, -2.75329455e-01,
                   4.27551222e+00, -3.74794018e+00, -3.65242484e+00,
                   3.20532031e+00, -1.73616130e+00,  4.15798946e+00,
                   1.17718220e+00, -1.04311069e+01, -4.09266896e+00,
                   1.41124899e+00, -7.37205126e-01,  5.25762998e+00,
                   1.19842461e+00, -1.84266774e+00,  1.32143804e+00,
                  -3.80872738e+00, -3.92448285e-01,  3.73841511e+00,
                  -7.10872944e+00,  2.99798639e+00,  2.06273459e+00,
                  -1.23043646e+00, -5.78853737e+00, -7.36284023e+00,
                   2.26225031e+00, -3.38355878e+00, -1.68746700e+00,
                  -6.06363654e+00, -2.99681162e+00,  1.51655389e+01,
                   5.85111732e+00,  3.67325563e+00, -3.88938332e+00,
                  -1.63657121e+00, -5.83800474e+00,  2.31465580e+00,
                   3.20496693e+00, -1.45495656e+00,  1.68808618e+00,
                  -9.41094585e-01,  7.22854336e+00, -9.81217137e+00,
                   2.66859888e+00, -1.47885682e+00, -9.04687110e+00,
                   8.09557449e+00, -8.42861449e+00, -2.62580838e+00,
                   5.11658218e+00, -1.52452654e+00, -1.96249233e+00,
                   5.97155920e+00, -1.75401929e+00,  1.06964882e+00,
                  -9.56683894e+00,  1.37675004e-01,  3.03911583e+00,
                  -1.13928638e+01, -6.36918611e+00,  2.05351791e+00,
                   1.90840417e+00, -5.13143543e+00,  8.82467194e+00,
                   5.66513682e+00, -9.15590476e-01, -1.54135558e+00,
                   8.13181157e+00, -1.21487209e+00,  6.03964686e-01,
                  -7.51586094e+00, -6.25207588e-01,  2.50537486e+00,
                   4.78314463e+00, -7.84010599e+00, -2.59846756e+00,
                   1.92095881e+00,  1.55754667e+00,  1.17162041e+01,
                  -6.93921261e+00, -3.61516358e+00,  2.10526659e+00,
                  -3.27262877e+00, -6.27686672e-01, -2.47391375e+00,
                   4.74857769e+00, -6.00001153e+00, -3.12236875e+00,
                  -2.05910641e+00, -1.47592926e+00, -1.52197710e+00,
                  -5.36219392e+00, -3.70460870e+00, -1.18081044e+00,
                   1.30067483e+00, -5.60363657e+00, -7.50442961e+00,
                   5.86388873e+00,  4.87562394e+00,  3.38591620e-01,
                   3.33931920e+00, -4.59088084e+00, -2.95116936e+00,
                   1.42467690e+00,  1.94647514e+00,  8.54062107e+00,
                  -1.77224155e+00,  1.77345100e-01, -4.87591385e+00,
                   4.13998676e-01,  3.76794944e+00,  4.22702123e+00,
                  -5.45522796e+00,  1.65271233e+00,  6.19622472e+00,
                   1.50604180e+00, -3.14617692e+00,  6.30024370e+00,
                  -7.21197086e+00,  6.01837982e+00, -7.52050511e+00,
                  -1.09395300e+00, -5.00216139e+00, -3.49358661e+00,
                   1.22685827e+01,  5.14362360e+00, -4.78872778e-01,
                   5.11733335e-01, -3.48664446e-01,  1.79755961e+00,
                   8.95215983e+00,  3.49282504e+00, -5.25135910e+00,
                  -2.85226951e+00, -1.13230869e+00, -5.81140476e+00,
                   3.73029644e-01,  6.57538675e+00,  2.16467890e+00,
                   6.90566193e+00,  1.40305875e+00, -7.24304684e+00,
                  -1.50332918e+00,  1.07448461e-01, -5.58793632e+00,
                   3.75489621e+00,  1.48970954e+00, -2.04834114e+00,
                   4.28431886e+00, -3.81467248e+00,  8.25504579e+00,
                  -5.16157750e+00, -4.55133425e+00,  5.41937050e+00,
                   1.22482918e+00, -1.61128396e+00, -3.58948123e+00,
                  -4.99342772e+00,  5.09773030e+00, -1.48636228e+00,
                  -5.56506361e+00,  7.50700635e+00,  2.68792959e+00,
                   2.20114723e+00,  2.84364223e+00, -5.95171067e+00,
                   2.25348726e+00,  2.22053252e+00, -5.10663431e-01,
                   1.25970172e+01, -6.86680266e+00,  3.39368931e+00,
                   6.52463646e+00, -6.07163044e+00,  1.41433456e+00,
                  -1.70006990e-01, -3.73880623e+00,  9.20656227e-01,
                   1.81601662e+00,  1.82045364e+00, -3.51682219e+00,
                  -1.38509221e+01,  2.35117304e+00]])
      • created_at :
        2020-06-10T17:34:00.243686
        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
        • school: 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])
        • school
          (school)
          <U16
          'Choate' ... 'Mt. Hermon'
          array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
                 'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype='<U16')
        • obs
          (chain, draw, school)
          float64
          -7.005 -13.43 ... -1.281 -4.613
          array([[[ -7.00515108, -13.43153612, -10.01040957, ..., -16.19090925,
                   -17.44132393, -20.0866369 ],
                  [ -6.86696896, -18.81725212,   9.65421384, ...,  16.53053917,
                     6.72465358, -24.18206066],
                  [114.025525  , -63.10320213, -17.18902305, ..., 100.29001401,
                   135.78625636,  67.50554246],
                  ...,
                  [-19.94832547, -14.52423533, -14.0245758 , ...,  -7.15475511,
                     8.34547408,   9.97533365],
                  [-13.62696997, -10.57929146, -45.13902796, ..., -16.99789642,
                   -10.53822116, -14.20868999],
                  [  3.48681755,  35.48027982,  42.72217281, ..., -33.83185313,
                    -1.28071988,  -4.61278391]]])
      • created_at :
        2020-06-10T17:34:00.249162
        arviz_version :
        0.8.3
        inference_library :
        pymc3
        inference_library_version :
        3.8

    • Show/Hide data repr Show/Hide attributes
      xarray.Dataset
        • school: 8
        • school
          (school)
          <U16
          'Choate' ... 'Mt. Hermon'
          array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
                 'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype='<U16')
        • obs
          (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 :
        2020-06-10T17:34:00.250446
        arviz_version :
        0.8.3
        inference_library :
        pymc3
        inference_library_version :
        3.8

[9]:
az.plot_trace(data);
../_images/notebooks_Introduction_14_0.png

Plotting with PyStan objects

ArviZ is built with first class support for PyStan objects, and can plot raw fit objects in a reasonable manner. Here is the same centered eight schools model:

[10]:
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[J];
}

model {
  mu ~ normal(0, 5);
  tau ~ cauchy(0, 5);
  theta ~ normal(mu, tau);
  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]);
    }
}
"""

schools_dat = {
    "J": 8,
    "y": [28, 8, -3, 7, -1, 1, 18, 12],
    "sigma": [15, 10, 16, 11, 9, 11, 10, 18],
}

sm = pystan.StanModel(model_code=schools_code, verbose=False)
fit = sm.sampling(data=schools_dat, iter=1000, chains=4)
INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_b0eada194ad938e30ed47926216f98ca NOW.
WARNING:pystan:18 of 2000 iterations ended with a divergence (0.9 %).
WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.
WARNING:pystan:Chain 2: E-BFMI = 0.193
WARNING:pystan:Chain 3: E-BFMI = 0.176
WARNING:pystan:E-BFMI below 0.2 indicates you may need to reparameterize your model
[11]:
az.plot_density(fit, var_names=["mu", "tau"]);
../_images/notebooks_Introduction_17_0.png

Again, converting to InferenceData (a netcdf datastore that loads data into xarray datasets), we can get much richer labelling and mixing of data. Here is a plot showing where the Hamiltonian sampler had divergences

[12]:
data = az.from_pystan(
    posterior=fit,
    posterior_predictive="y_hat",
    observed_data=["y"],
    log_likelihood={"y": "log_lik"},
    coords={"school": schools},
    dims={
        "theta": ["school"],
        "y": ["school"],
        "log_lik": ["school"],
        "y_hat": ["school"],
        "theta_tilde": ["school"],
    },
)
data
[12]:
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)
          <U16
          'Choate' ... 'Mt. Hermon'
          array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
                 'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype='<U16')
        • mu
          (chain, draw)
          float64
          5.1 5.565 5.362 ... 3.331 2.2 2.327
          array([[ 5.10040709,  5.56526385,  5.3618364 , ...,  5.06734909,
                   3.40778873,  2.69909761],
                 [ 3.25671658,  2.00700677,  2.69667926, ...,  2.92315733,
                   3.73205842,  3.69622906],
                 [ 5.06802039,  2.26509343,  2.87166717, ...,  2.11407466,
                   4.81741353,  7.3519171 ],
                 [ 0.1038528 , -0.09374646, -0.28283904, ...,  3.33102952,
                   2.20015266,  2.32721317]])
        • tau
          (chain, draw)
          float64
          1.202 2.231 1.327 ... 20.19 11.85
          array([[ 1.20212821,  2.23069646,  1.32669804, ...,  1.07703112,
                   1.87183738,  1.75443014],
                 [ 1.25900468,  1.63896675,  1.46146098, ...,  0.59632991,
                   0.58807019,  0.5944897 ],
                 [ 0.74925633,  0.71955362,  0.59900204, ...,  4.39631868,
                   1.87395808,  3.66925351],
                 [ 0.64854989,  0.56661867,  0.55010696, ..., 11.23778771,
                  20.19192096, 11.8460885 ]])
        • theta
          (chain, draw, school)
          float64
          5.268 5.037 4.21 ... 14.36 3.22
          array([[[  5.26795905,   5.03707292,   4.21035211, ...,   5.93199746,
                     7.22942443,   4.76278775],
                  [  5.59672759,   5.05357139,   6.26365386, ...,   4.15659256,
                     2.95644306,   6.2024757 ],
                  [  5.0123936 ,   5.20823416,   4.25580892, ...,   6.003762  ,
                     6.96505472,   4.2518585 ],
                  ...,
                  [  4.08224287,   5.46704104,   5.79343569, ...,   3.6970148 ,
                     6.86174954,   6.85895359],
                  [  5.41487964,   3.56785377,   2.69235867, ...,   6.37334377,
                     2.53291894,   3.18463374],
                  [  2.87002693,   4.11246062,   3.72243438, ...,   1.32983962,
                     5.6719599 ,   4.53813603]],
          
                 [[  2.51482793,   3.30753964,   2.41482108, ...,   0.44359836,
                     4.1190871 ,   4.25398038],
                  [  3.99947947,   2.40409008,   3.16220843, ...,   4.68306225,
                     2.46867937,   1.482205  ],
                  [  3.207702  ,   2.81189848,   4.17111688, ...,   5.12158726,
                     1.77020089,   2.78709132],
                  ...,
                  [  3.49299364,   3.2849658 ,   3.96773018, ...,   2.52228923,
                     2.248126  ,   3.30709396],
                  [  3.71134003,   3.65395977,   2.93835064, ...,   4.14588605,
                     4.4270301 ,   2.89136813],
                  [  4.71327614,   3.53783826,   4.01350509, ...,   4.00573384,
                     3.8171959 ,   4.32287278]],
          
                 [[  5.30897754,   4.73651815,   5.75086504, ...,   5.42648964,
                     4.21368951,   4.49280385],
                  [  2.21058763,   2.34034814,   3.92649465, ...,   2.90681141,
                     2.0888858 ,   2.41656732],
                  [  2.44914824,   2.60384926,   2.40744517, ...,   2.31484192,
                     2.41159948,   2.7324515 ],
                  ...,
                  [  8.66912663,   1.512115  ,   2.45966974, ...,   7.22779168,
                     3.77851803,   3.6482612 ],
                  [  7.24713517,   4.59569558,   5.02705348, ...,   3.79556901,
                     6.98287389,   6.38335082],
                  [  4.29268803,   6.08441733,   4.14177454, ...,   4.9925426 ,
                     4.40638394,   3.50908264]],
          
                 [[ -0.09199175,   0.49842581,  -0.53020596, ...,  -0.0787323 ,
                    -0.54140645,  -0.17915019],
                  [ -0.50218323,   0.31870224,  -0.405048  , ...,  -0.28376237,
                    -0.34162476,   0.07373626],
                  [  0.30515502,  -0.29777416,  -0.20006018, ...,   0.18788433,
                    -0.49743822,  -0.0742338 ],
                  ...,
                  [ 10.15375968,  21.748118  ,  -4.5702728 , ...,   5.47191682,
                    -0.40721312,  -9.44280244],
                  [ 32.23656165,  -1.86894125,  -1.08065556, ..., -11.01646021,
                    16.20578347,  -1.2524635 ],
                  [ 16.94073406,   2.22438863,  -2.06371558, ...,  -5.02911752,
                    14.36029172,   3.22044715]]])
      • created_at :
        2020-06-10T17:35:53.760020
        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: 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)
          <U16
          'Choate' ... 'Mt. Hermon'
          array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
                 'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype='<U16')
        • y_hat
          (chain, draw, school)
          float64
          -6.037 9.903 14.01 ... 43.57 28.42
          array([[[ -6.0374751 ,   9.90291358,  14.01138981, ...,   5.59146304,
                     7.54330337,  -4.2737839 ],
                  [  3.23935084,   7.52806977,  22.7911258 , ...,  -8.86228559,
                     4.18210178,  22.29583022],
                  [  0.43456908,   2.36580065,  -1.0379147 , ...,  -2.11559449,
                     7.49674662, -21.8299887 ],
                  ...,
                  [-23.37387803,  -4.25993853,  10.16982717, ...,  -7.75839332,
                    11.65177613,  -1.57133793],
                  [ 35.91084599,   2.11345529,  -1.84769022, ...,  24.76079116,
                    -9.83201554,   7.11101976],
                  [  3.3266679 ,  -0.50842836,   6.63333991, ...,  11.2513764 ,
                     9.90970093,  -3.04506755]],
          
                 [[  6.45223865,   7.66043625,  13.19122882, ...,  -8.68536593,
                    16.75227912,  -2.94953571],
                  [-17.21574436,  15.28594632,  18.69754036, ...,  21.8577613 ,
                    16.34692255,  16.38001936],
                  [ 24.5484029 ,   3.65262266,  -2.04993822, ...,   6.89159587,
                    15.5594578 ,   1.3728226 ],
                  ...,
                  [-10.32319932,  -0.89060054,  -4.31425555, ...,  -6.25797114,
                     8.71613195,   1.30431368],
                  [ 14.13249493,   3.26153202,  15.07045584, ...,  -1.18512082,
                     8.13919735,   7.21193093],
                  [ 29.38087964, -22.07437273,  31.9967746 , ...,  10.73434552,
                     2.34347059,  39.06602106]],
          
                 [[  7.15692832,  12.3045443 ,  20.37800831, ...,   3.40777519,
                    12.38504667,  12.207693  ],
                  [ 12.14688069,  -9.51329437, -14.80031082, ...,  -6.10742988,
                     6.44135824, -13.40090849],
                  [ 16.68112235,  10.34264465,  -1.650218  , ...,  10.15265282,
                   -26.03093955,  33.45995267],
                  ...,
                  [ 14.99861038,  -0.88997479,   9.97722446, ..., -11.70954208,
                    -0.93394289,   0.69076047],
                  [ 12.72793049,  13.72292366,   1.02311483, ...,  12.54074923,
                    21.63232645, -16.77657839],
                  [ 35.24036631,   5.66656187,  30.84014673, ...,  19.07910288,
                     9.88245398,  -4.85000145]],
          
                 [[ 36.13008019,  11.51137938, -12.11040594, ...,  -4.0937036 ,
                    -4.57824307,   3.62960921],
                  [ -4.4996811 ,  -4.227572  , -16.70268441, ..., -13.19581623,
                   -10.44766931, -16.78910203],
                  [-16.05075926,  -3.41570814, -19.07427617, ...,  10.16666467,
                    11.56985678,  -6.56313687],
                  ...,
                  [ 17.4705099 ,  23.92588795,  -9.50090652, ...,   6.58297516,
                     0.14891797,  -6.52292138],
                  [ 22.05341924,  -9.44319588,  23.89624321, ..., -17.92626387,
                    15.3780051 , -10.24854644],
                  [ 22.31591907,   7.32171248,   4.96743133, ..., -23.63981518,
                    43.56503648,  28.41901104]]])
      • created_at :
        2020-06-10T17:35:53.777987
        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: 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)
          <U16
          'Choate' ... 'Mt. Hermon'
          array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
                 'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype='<U16')
        • y
          (chain, draw, school)
          float64
          -4.775 -3.265 ... -3.288 -3.928
          array([[[-4.77531248, -3.26541831, -3.79306862, ..., -3.41734868,
                   -3.80155012, -3.89013937],
                  [-4.74233677, -3.26493083, -3.85913523, ..., -3.35800768,
                   -4.35306665, -3.86117956],
                  [-4.80127773, -3.26049341, -3.79435296, ..., -3.4202951 ,
                   -3.83037371, -3.90195488],
                  ...,
                  [-4.89823119, -3.25360303, -3.84255169, ..., -3.3468912 ,
                   -3.84182674, -3.85009788],
                  [-4.76051687, -3.31974323, -3.75481426, ..., -3.43614299,
                   -4.41767661, -3.92923418],
                  [-5.03035662, -3.29708844, -3.77979117, ..., -3.31728337,
                   -3.98142649, -3.89523531]],
          
                 [[-5.07030872, -3.33161955, -3.74879344, ..., -3.31811307,
                   -4.18492234, -3.90190415],
                  [-4.90704426, -3.37809467, -3.76569291, ..., -3.37288731,
                   -4.42763323, -3.98002636],
                  [-4.99289549, -3.35610561, -3.79196655, ..., -3.38703001,
                   -4.53855552, -3.94029437],
                  ...,
                  [-4.96164065, -3.33268136, -3.78635004, ..., -3.32640969,
                   -4.4621313 , -3.92592544],
                  [-4.9379643 , -3.31596395, -3.76040227, ..., -3.35772884,
                   -4.14265119, -3.93734605],
                  [-4.83203653, -3.32107806, -3.78760002, ..., -3.35416619,
                   -4.22728329, -3.90026443]],
          
                 [[-4.77117207, -3.2747752 , -3.84109296, ..., -3.39779997,
                   -4.17183541, -3.8962825 ],
                  [-5.10497494, -3.38168192, -3.78523102, ..., -3.33185831,
                   -4.4873414 , -3.95104205],
                  [-5.07775768, -3.36711584, -3.74863754, ..., -3.32397765,
                   -4.43651478, -3.94185266],
                  ...,
                  [-4.45739466, -3.43198689, -3.74974599, ..., -3.47710401,
                   -4.23277637, -3.91695156],
                  [-4.58405851, -3.27947007, -3.81737411, ..., -3.34912805,
                   -3.82840897, -3.85799354],
                  [-4.87595905, -3.23987091, -3.79114629, ..., -3.38270321,
                   -4.14545561, -3.92056905]],
          
                 [[-5.38067762, -3.5028917 , -3.70344109, ..., -3.32164233,
                   -4.94044239, -4.03821723],
                  [-5.43226529, -3.5165353 , -3.70467916, ..., -3.32364391,
                   -4.90359962, -4.02880993],
                  [-5.33144304, -3.56578891, -3.7068391 , ..., -3.31955914,
                   -4.93229973, -4.03429042],
                  ...,
                  [-4.3347405 , -4.16657737, -3.69634319, ..., -3.39947034,
                   -4.9156511 , -4.51886859],
                  [-3.66687419, -3.70850363, -3.69872234, ..., -3.91350867,
                   -3.23761969, -4.08034083],
                  [-3.89878287, -3.38831206, -3.69323942, ..., -3.46704148,
                   -3.28776101, -3.92826175]]])
      • created_at :
        2020-06-10T17:35:53.774312
        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: 500
        • 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])
        • accept_stat
          (chain, draw)
          float64
          0.8343 0.4552 ... 0.9836 0.9973
          array([[0.83427208, 0.45522566, 0.96624807, ..., 0.77208011, 0.16547731,
                  0.82547175],
                 [0.99681883, 0.95244552, 0.99394157, ..., 0.88393096, 0.90840264,
                  1.        ],
                 [0.08367187, 0.85771457, 1.        , ..., 0.9810016 , 0.99080896,
                  0.95907463],
                 [0.93085341, 0.34875619, 0.59818615, ..., 0.99211124, 0.98364323,
                  0.99731371]])
        • stepsize
          (chain, draw)
          float64
          0.1733 0.1733 ... 0.1188 0.1188
          array([[0.17333576, 0.17333576, 0.17333576, ..., 0.17333576, 0.17333576,
                  0.17333576],
                 [0.07970539, 0.07970539, 0.07970539, ..., 0.07970539, 0.07970539,
                  0.07970539],
                 [0.06778361, 0.06778361, 0.06778361, ..., 0.06778361, 0.06778361,
                  0.06778361],
                 [0.11879204, 0.11879204, 0.11879204, ..., 0.11879204, 0.11879204,
                  0.11879204]])
        • treedepth
          (chain, draw)
          int64
          3 3 3 3 3 3 4 4 ... 6 5 5 6 6 5 6 5
          array([[3, 3, 3, ..., 4, 3, 3],
                 [4, 4, 4, ..., 3, 3, 3],
                 [4, 5, 3, ..., 5, 5, 5],
                 [5, 1, 2, ..., 5, 6, 5]])
        • n_leapfrog
          (chain, draw)
          int64
          7 7 7 7 7 7 ... 31 63 63 31 63 31
          array([[ 7,  7,  7, ..., 27,  7,  7],
                 [15, 15, 15, ...,  7,  7, 15],
                 [31, 55,  7, ..., 63, 31, 31],
                 [47,  3,  3, ..., 31, 63, 31]])
        • 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
          10.21 13.93 13.44 ... 32.73 28.14
          array([[10.20693978, 13.93085747, 13.43521926, ..., 12.29495316,
                  13.46605921, 14.22549271],
                 [13.17818175, 11.37017914, 11.42654959, ...,  7.01892776,
                   8.87263573,  7.8678977 ],
                 [ 5.98879364,  9.22839116,  5.70304851, ..., 22.97114689,
                  18.60193693, 18.31306761],
                 [ 6.74956591,  4.81455757,  7.11467086, ..., 29.5590906 ,
                  32.72527458, 28.13558373]])
        • lp
          (chain, draw)
          float64
          -6.744 -10.6 ... -27.28 -22.17
          array([[ -6.74356275, -10.59971097,  -7.06732632, ...,  -8.22004983,
                  -10.26028264,  -9.80641468],
                 [ -8.51908224,  -9.40025125,  -8.55896875, ...,  -3.50197584,
                   -6.0401085 ,  -1.78208431],
                 [ -2.91168133,  -4.44647935,  -1.40061324, ..., -15.52248756,
                  -12.78328387, -16.1222584 ],
                 [ -3.69751253,  -2.05491867,  -3.47644376, ..., -26.47544111,
                  -27.27571599, -22.17195889]])
      • created_at :
        2020-06-10T17:35:53.768327
        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)
          <U16
          'Choate' ... 'Mt. Hermon'
          array(['Choate', 'Deerfield', 'Phillips Andover', 'Phillips Exeter',
                 'Hotchkiss', 'Lawrenceville', "St. Paul's", 'Mt. Hermon'], dtype='<U16')
        • y
          (school)
          int64
          28 8 -3 7 -1 1 18 12
          array([28,  8, -3,  7, -1,  1, 18, 12])
      • created_at :
        2020-06-10T17:35:53.754942
        arviz_version :
        0.8.3
        inference_library :
        pystan
        inference_library_version :
        2.19.1.1

[13]:
az.plot_pair(
    data,
    coords={"school": ["Choate", "Deerfield", "Phillips Andover"]},
    divergences=True,
);
../_images/notebooks_Introduction_20_0.png