ArviZ Quickstart
Set-up
Here we add the necessary packages for this notebook and load a few we will use throughout.
using ArviZ, ArviZPythonPlots, Distributions, LinearAlgebra, Random, StanSample, Turing CondaPkg Found dependencies: /home/runner/.julia/packages/DimensionalData/48C1z/CondaPkg.toml
CondaPkg Found dependencies: /home/runner/.julia/packages/PythonCall/avYrV/CondaPkg.toml
CondaPkg Found dependencies: /home/runner/.julia/packages/ArviZPythonPlots/TzoLB/CondaPkg.toml
CondaPkg Found dependencies: /home/runner/.julia/packages/PythonPlot/oS8x4/CondaPkg.toml
CondaPkg Resolving changes
+ arviz
+ libstdcxx-ng
+ matplotlib
+ numpy
+ openssl
+ pandas
+ python
+ xarray
CondaPkg Initialising pixi
│ /home/runner/.julia/artifacts/cefba4912c2b400756d043a2563ef77a0088866b/bin/pixi
│ init
│ --format pixi
└ /home/runner/work/ArviZ.jl/ArviZ.jl/docs/.CondaPkg
✔ Created /home/runner/work/ArviZ.jl/ArviZ.jl/docs/.CondaPkg/pixi.toml
CondaPkg Wrote /home/runner/work/ArviZ.jl/ArviZ.jl/docs/.CondaPkg/pixi.toml
│ [dependencies]
│ openssl = ">=3, <3.6, >=3, <3.6"
│ libstdcxx-ng = ">=3.4,<15.0"
│ matplotlib = ">=1"
│ pandas = "*"
│ xarray = "*"
│ arviz = ">=0.15.0,<=0.18"
│ numpy = "*"
│
│ [dependencies.python]
│ channel = "conda-forge"
│ build = "*cpython*"
│ version = ">=3.8,<4"
│
│ [project]
│ name = ".CondaPkg"
│ platforms = ["linux-64"]
│ channels = ["conda-forge"]
│ channel-priority = "strict"
└ description = "automatically generated by CondaPkg.jl"
CondaPkg Installing packages
│ /home/runner/.julia/artifacts/cefba4912c2b400756d043a2563ef77a0088866b/bin/pixi
│ install
└ --manifest-path /home/runner/work/ArviZ.jl/ArviZ.jl/docs/.CondaPkg/pixi.toml
✔ The default environment has been installed.# ArviZPythonPlots ships with style sheets!
use_style("arviz-darkgrid")Get started with plotting
To plot with ArviZ, we need to load the ArviZPythonPlots package. ArviZ is designed to be used with libraries like Stan, Turing.jl, and Soss.jl but works fine with raw arrays.
rng1 = Random.MersenneTwister(37772);plot_posterior(randn(rng1, 100_000));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.
s = (50, 10)
plot_forest((
normal=randn(rng1, s),
gumbel=rand(rng1, Gumbel(), s),
student_t=rand(rng1, TDist(6), s),
exponential=rand(rng1, Exponential(), s),
));Plotting with MCMCChains.jl’s Chains objects produced by Turing.jl
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, I give the schools the names of a different eight schools.
This model is small enough to write down, is hierarchical, and uses labelling. Additionally, a centered parameterization causes divergences (which are interesting for illustration).
First we create our data and set some sampling parameters.
J = 8
y = [28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0]
σ = [15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0]
schools = [
"Choate",
"Deerfield",
"Phillips Andover",
"Phillips Exeter",
"Hotchkiss",
"Lawrenceville",
"St. Paul's",
"Mt. Hermon",
]
ndraws = 1_000
ndraws_warmup = 1_000
nchains = 4;Now we write and run the model using Turing:
Turing.@model function model_turing(y, σ, J=length(y))
μ ~ Normal(0, 5)
τ ~ truncated(Cauchy(0, 5), 0, Inf)
θ ~ filldist(Normal(μ, τ), J)
for i in 1:J
y[i] ~ Normal(θ[i], σ[i])
end
end;rng2 = Random.MersenneTwister(16653);param_mod_turing = model_turing(y, σ)
sampler = NUTS(ndraws_warmup, 0.8)
turing_chns = Turing.sample(
rng2, model_turing(y, σ), sampler, MCMCThreads(), ndraws, nchains
);Sampling (2 threads) 0%| | ETA: N/A
┌ Info: Found initial step size
└ ϵ = 0.2
┌ Info: Found initial step size
└ ϵ = 0.41250000000000003
Sampling (2 threads) 0%|▏ | ETA: 0:47:39
Sampling (2 threads) 1%|▎ | ETA: 0:23:44
Sampling (2 threads) 2%|▌ | ETA: 0:15:45
Sampling (2 threads) 2%|▋ | ETA: 0:11:46
Sampling (2 threads) 2%|▊ | ETA: 0:09:23
Sampling (2 threads) 3%|▉ | ETA: 0:07:47
Sampling (2 threads) 4%|█ | ETA: 0:06:38
Sampling (2 threads) 4%|█▎ | ETA: 0:05:47
Sampling (2 threads) 4%|█▍ | ETA: 0:05:07
Sampling (2 threads) 5%|█▌ | ETA: 0:04:35
Sampling (2 threads) 6%|█▋ | ETA: 0:04:09
Sampling (2 threads) 6%|█▊ | ETA: 0:03:47
Sampling (2 threads) 6%|██ | ETA: 0:03:29
Sampling (2 threads) 7%|██▏ | ETA: 0:03:13
Sampling (2 threads) 8%|██▎ | ETA: 0:02:59
Sampling (2 threads) 8%|██▍ | ETA: 0:02:47
Sampling (2 threads) 8%|██▌ | ETA: 0:02:36
Sampling (2 threads) 9%|██▊ | ETA: 0:02:27
Sampling (2 threads) 10%|██▉ | ETA: 0:02:19
Sampling (2 threads) 10%|███ | ETA: 0:02:11
Sampling (2 threads) 10%|███▏ | ETA: 0:02:04
Sampling (2 threads) 11%|███▎ | ETA: 0:01:58
Sampling (2 threads) 12%|███▌ | ETA: 0:01:52
Sampling (2 threads) 12%|███▋ | ETA: 0:01:47
Sampling (2 threads) 12%|███▊ | ETA: 0:01:42
Sampling (2 threads) 13%|███▉ | ETA: 0:01:38
Sampling (2 threads) 14%|████ | ETA: 0:01:33
Sampling (2 threads) 14%|████▎ | ETA: 0:01:30
Sampling (2 threads) 14%|████▍ | ETA: 0:01:26
Sampling (2 threads) 15%|████▌ | ETA: 0:01:23
Sampling (2 threads) 16%|████▋ | ETA: 0:01:20
Sampling (2 threads) 16%|████▊ | ETA: 0:01:17
Sampling (2 threads) 16%|█████ | ETA: 0:01:14
Sampling (2 threads) 17%|█████▏ | ETA: 0:01:11
Sampling (2 threads) 18%|█████▎ | ETA: 0:01:09
Sampling (2 threads) 18%|█████▍ | ETA: 0:01:07
Sampling (2 threads) 18%|█████▌ | ETA: 0:01:05
Sampling (2 threads) 19%|█████▊ | ETA: 0:01:02
Sampling (2 threads) 20%|█████▉ | ETA: 0:01:01
Sampling (2 threads) 20%|██████ | ETA: 0:00:59
Sampling (2 threads) 20%|██████▏ | ETA: 0:00:57
Sampling (2 threads) 21%|██████▎ | ETA: 0:00:55
Sampling (2 threads) 22%|██████▌ | ETA: 0:00:54
Sampling (2 threads) 22%|██████▋ | ETA: 0:00:52
Sampling (2 threads) 22%|██████▊ | ETA: 0:00:51
Sampling (2 threads) 23%|██████▉ | ETA: 0:00:50
Sampling (2 threads) 24%|███████ | ETA: 0:00:48
Sampling (2 threads) 24%|███████▎ | ETA: 0:00:47
Sampling (2 threads) 24%|███████▍ | ETA: 0:00:46
Sampling (2 threads) 25%|███████▌ | ETA: 0:00:44
Sampling (2 threads) 26%|███████▋ | ETA: 0:00:43
Sampling (2 threads) 26%|███████▊ | ETA: 0:00:42
Sampling (2 threads) 26%|████████ | ETA: 0:00:41
Sampling (2 threads) 27%|████████▏ | ETA: 0:00:40
Sampling (2 threads) 28%|████████▎ | ETA: 0:00:39
Sampling (2 threads) 28%|████████▍ | ETA: 0:00:38
Sampling (2 threads) 28%|████████▌ | ETA: 0:00:37
Sampling (2 threads) 29%|████████▊ | ETA: 0:00:36
Sampling (2 threads) 30%|████████▉ | ETA: 0:00:36
Sampling (2 threads) 30%|█████████ | ETA: 0:00:35
Sampling (2 threads) 30%|█████████▏ | ETA: 0:00:34
Sampling (2 threads) 31%|█████████▎ | ETA: 0:00:33
Sampling (2 threads) 32%|█████████▌ | ETA: 0:00:32
Sampling (2 threads) 32%|█████████▋ | ETA: 0:00:32
Sampling (2 threads) 32%|█████████▊ | ETA: 0:00:31
Sampling (2 threads) 33%|█████████▉ | ETA: 0:00:30
Sampling (2 threads) 34%|██████████ | ETA: 0:00:30
Sampling (2 threads) 34%|██████████▎ | ETA: 0:00:29
Sampling (2 threads) 34%|██████████▍ | ETA: 0:00:28
Sampling (2 threads) 35%|██████████▌ | ETA: 0:00:28
Sampling (2 threads) 36%|██████████▋ | ETA: 0:00:27
Sampling (2 threads) 36%|██████████▊ | ETA: 0:00:27
Sampling (2 threads) 36%|███████████ | ETA: 0:00:26
Sampling (2 threads) 37%|███████████▏ | ETA: 0:00:26
Sampling (2 threads) 38%|███████████▎ | ETA: 0:00:25
Sampling (2 threads) 38%|███████████▍ | ETA: 0:00:24
Sampling (2 threads) 38%|███████████▌ | ETA: 0:00:24
Sampling (2 threads) 39%|███████████▊ | ETA: 0:00:23
Sampling (2 threads) 40%|███████████▉ | ETA: 0:00:23
Sampling (2 threads) 40%|████████████ | ETA: 0:00:23
Sampling (2 threads) 40%|████████████▏ | ETA: 0:00:22
Sampling (2 threads) 41%|████████████▎ | ETA: 0:00:22
Sampling (2 threads) 42%|████████████▌ | ETA: 0:00:21
Sampling (2 threads) 42%|████████████▋ | ETA: 0:00:21
Sampling (2 threads) 42%|████████████▊ | ETA: 0:00:20
Sampling (2 threads) 43%|████████████▉ | ETA: 0:00:20
Sampling (2 threads) 44%|█████████████ | ETA: 0:00:20
Sampling (2 threads) 44%|█████████████▎ | ETA: 0:00:23
Sampling (2 threads) 44%|█████████████▍ | ETA: 0:00:23
┌ Info: Found initial step size
└ ϵ = 1.0
Sampling (2 threads) 45%|█████████████▌ | ETA: 0:00:22
Sampling (2 threads) 46%|█████████████▋ | ETA: 0:00:22
Sampling (2 threads) 46%|█████████████▊ | ETA: 0:00:21
Sampling (2 threads) 46%|██████████████ | ETA: 0:00:21
Sampling (2 threads) 47%|██████████████▏ | ETA: 0:00:21
Sampling (2 threads) 48%|██████████████▎ | ETA: 0:00:20
Sampling (2 threads) 48%|██████████████▍ | ETA: 0:00:20
Sampling (2 threads) 48%|██████████████▌ | ETA: 0:00:19
Sampling (2 threads) 49%|██████████████▊ | ETA: 0:00:19
Sampling (2 threads) 50%|██████████████▉ | ETA: 0:00:19
Sampling (2 threads) 50%|███████████████ | ETA: 0:00:18
Sampling (2 threads) 50%|███████████████▏ | ETA: 0:00:18
Sampling (2 threads) 51%|███████████████▎ | ETA: 0:00:18
Sampling (2 threads) 52%|███████████████▌ | ETA: 0:00:17
Sampling (2 threads) 52%|███████████████▋ | ETA: 0:00:17
Sampling (2 threads) 52%|███████████████▊ | ETA: 0:00:17
Sampling (2 threads) 53%|███████████████▉ | ETA: 0:00:16
Sampling (2 threads) 54%|████████████████ | ETA: 0:00:16
Sampling (2 threads) 54%|████████████████▎ | ETA: 0:00:16
Sampling (2 threads) 55%|████████████████▍ | ETA: 0:00:15
Sampling (2 threads) 55%|████████████████▌ | ETA: 0:00:15
Sampling (2 threads) 56%|████████████████▋ | ETA: 0:00:15
Sampling (2 threads) 56%|████████████████▊ | ETA: 0:00:15
Sampling (2 threads) 56%|█████████████████ | ETA: 0:00:14
Sampling (2 threads) 57%|█████████████████▏ | ETA: 0:00:14
Sampling (2 threads) 57%|█████████████████▎ | ETA: 0:00:14
┌ Info: Found initial step size
└ ϵ = 0.2
Sampling (2 threads) 58%|█████████████████▍ | ETA: 0:00:13
Sampling (2 threads) 58%|█████████████████▌ | ETA: 0:00:13
Sampling (2 threads) 59%|█████████████████▊ | ETA: 0:00:13
Sampling (2 threads) 60%|█████████████████▉ | ETA: 0:00:13
Sampling (2 threads) 60%|██████████████████ | ETA: 0:00:12
Sampling (2 threads) 60%|██████████████████▏ | ETA: 0:00:12
Sampling (2 threads) 61%|██████████████████▎ | ETA: 0:00:12
Sampling (2 threads) 62%|██████████████████▌ | ETA: 0:00:12
Sampling (2 threads) 62%|██████████████████▋ | ETA: 0:00:11
Sampling (2 threads) 62%|██████████████████▊ | ETA: 0:00:11
Sampling (2 threads) 63%|██████████████████▉ | ETA: 0:00:11
Sampling (2 threads) 64%|███████████████████ | ETA: 0:00:11
Sampling (2 threads) 64%|███████████████████▎ | ETA: 0:00:10
Sampling (2 threads) 64%|███████████████████▍ | ETA: 0:00:10
Sampling (2 threads) 65%|███████████████████▌ | ETA: 0:00:10
Sampling (2 threads) 66%|███████████████████▋ | ETA: 0:00:10
Sampling (2 threads) 66%|███████████████████▊ | ETA: 0:00:10
Sampling (2 threads) 66%|████████████████████ | ETA: 0:00:09
Sampling (2 threads) 67%|████████████████████▏ | ETA: 0:00:09
Sampling (2 threads) 68%|████████████████████▎ | ETA: 0:00:09
Sampling (2 threads) 68%|████████████████████▍ | ETA: 0:00:09
Sampling (2 threads) 68%|████████████████████▌ | ETA: 0:00:09
Sampling (2 threads) 69%|████████████████████▊ | ETA: 0:00:08
Sampling (2 threads) 70%|████████████████████▉ | ETA: 0:00:08
Sampling (2 threads) 70%|█████████████████████ | ETA: 0:00:08
Sampling (2 threads) 70%|█████████████████████▏ | ETA: 0:00:08
Sampling (2 threads) 71%|█████████████████████▎ | ETA: 0:00:08
Sampling (2 threads) 72%|█████████████████████▌ | ETA: 0:00:07
Sampling (2 threads) 72%|█████████████████████▋ | ETA: 0:00:07
Sampling (2 threads) 72%|█████████████████████▊ | ETA: 0:00:07
Sampling (2 threads) 73%|█████████████████████▉ | ETA: 0:00:07
Sampling (2 threads) 74%|██████████████████████ | ETA: 0:00:07
Sampling (2 threads) 74%|██████████████████████▎ | ETA: 0:00:07
Sampling (2 threads) 74%|██████████████████████▍ | ETA: 0:00:06
Sampling (2 threads) 75%|██████████████████████▌ | ETA: 0:00:06
Sampling (2 threads) 76%|██████████████████████▋ | ETA: 0:00:06
Sampling (2 threads) 76%|██████████████████████▊ | ETA: 0:00:06
Sampling (2 threads) 76%|███████████████████████ | ETA: 0:00:06
Sampling (2 threads) 77%|███████████████████████▏ | ETA: 0:00:06
Sampling (2 threads) 78%|███████████████████████▎ | ETA: 0:00:05
Sampling (2 threads) 78%|███████████████████████▍ | ETA: 0:00:05
Sampling (2 threads) 78%|███████████████████████▌ | ETA: 0:00:05
Sampling (2 threads) 79%|███████████████████████▊ | ETA: 0:00:05
Sampling (2 threads) 80%|███████████████████████▉ | ETA: 0:00:05
Sampling (2 threads) 80%|████████████████████████ | ETA: 0:00:05
Sampling (2 threads) 80%|████████████████████████▏ | ETA: 0:00:05
Sampling (2 threads) 81%|████████████████████████▎ | ETA: 0:00:04
Sampling (2 threads) 82%|████████████████████████▌ | ETA: 0:00:04
Sampling (2 threads) 82%|████████████████████████▋ | ETA: 0:00:04
Sampling (2 threads) 82%|████████████████████████▊ | ETA: 0:00:04
Sampling (2 threads) 83%|████████████████████████▉ | ETA: 0:00:04
Sampling (2 threads) 84%|█████████████████████████ | ETA: 0:00:04
Sampling (2 threads) 84%|█████████████████████████▎ | ETA: 0:00:04
Sampling (2 threads) 84%|█████████████████████████▍ | ETA: 0:00:03
Sampling (2 threads) 85%|█████████████████████████▌ | ETA: 0:00:03
Sampling (2 threads) 86%|█████████████████████████▋ | ETA: 0:00:03
Sampling (2 threads) 86%|█████████████████████████▊ | ETA: 0:00:03
Sampling (2 threads) 86%|██████████████████████████ | ETA: 0:00:03
Sampling (2 threads) 87%|██████████████████████████▏ | ETA: 0:00:03
Sampling (2 threads) 88%|██████████████████████████▎ | ETA: 0:00:03
Sampling (2 threads) 88%|██████████████████████████▍ | ETA: 0:00:03
Sampling (2 threads) 88%|██████████████████████████▌ | ETA: 0:00:02
Sampling (2 threads) 89%|██████████████████████████▊ | ETA: 0:00:02
Sampling (2 threads) 90%|██████████████████████████▉ | ETA: 0:00:02
Sampling (2 threads) 90%|███████████████████████████ | ETA: 0:00:02
Sampling (2 threads) 90%|███████████████████████████▏ | ETA: 0:00:02
Sampling (2 threads) 91%|███████████████████████████▎ | ETA: 0:00:02
Sampling (2 threads) 92%|███████████████████████████▌ | ETA: 0:00:02
Sampling (2 threads) 92%|███████████████████████████▋ | ETA: 0:00:02
Sampling (2 threads) 92%|███████████████████████████▊ | ETA: 0:00:02
Sampling (2 threads) 93%|███████████████████████████▉ | ETA: 0:00:01
Sampling (2 threads) 94%|████████████████████████████ | ETA: 0:00:01
Sampling (2 threads) 94%|████████████████████████████▎ | ETA: 0:00:01
Sampling (2 threads) 94%|████████████████████████████▍ | ETA: 0:00:01
Sampling (2 threads) 95%|████████████████████████████▌ | ETA: 0:00:01
Sampling (2 threads) 96%|████████████████████████████▋ | ETA: 0:00:01
Sampling (2 threads) 96%|████████████████████████████▊ | ETA: 0:00:01
Sampling (2 threads) 96%|█████████████████████████████ | ETA: 0:00:01
Sampling (2 threads) 97%|█████████████████████████████▏| ETA: 0:00:01
Sampling (2 threads) 98%|█████████████████████████████▎| ETA: 0:00:00
Sampling (2 threads) 98%|█████████████████████████████▍| ETA: 0:00:00
Sampling (2 threads) 98%|█████████████████████████████▌| ETA: 0:00:00
Sampling (2 threads) 99%|█████████████████████████████▊| ETA: 0:00:00
Sampling (2 threads) 100%|█████████████████████████████▉| ETA: 0:00:00
Sampling (2 threads) 100%|██████████████████████████████| Time: 0:00:19
Sampling (2 threads) 100%|██████████████████████████████| Time: 0:00:19Most ArviZ functions work fine with Chains objects from Turing:
plot_autocorr(turing_chns; var_names=(:μ, :τ));Convert to InferenceData
For much more powerful querying, analysis and plotting, we can use built-in ArviZ utilities to convert Chains objects to multidimensional data structures with named dimensions and indices. Note that for such dimensions, the information is not contained in Chains, so we need to provide it.
ArviZ is built to work with InferenceData, and the more groups it has access to, the more powerful analyses it can perform.
idata_turing_post = from_mcmcchains(
turing_chns;
coords=(; school=schools),
dims=NamedTuple(k => (:school,) for k in (:y, :σ, :θ)),
library="Turing",
)InferenceData
posterior
┌ 1000×4×8 Dataset ┐ ├──────────────────┴──────────────────────────────────────────── dims ┐ ↓ draw, → chain, ↗ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered ├───────────────────────────────────────────────────────────── layers ┤ :μ eltype: Float64 dims: draw, chain size: 1000×4 :τ eltype: Float64 dims: draw, chain size: 1000×4 :θ eltype: Float64 dims: draw, chain, school size: 1000×4×8 ├─────────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 2 entries: "created_at" => "2025-08-19T09:39:52.91" "inference_library" => "Turing"
sample_stats
┌ 1000×4 Dataset ┐ ├────────────────┴──────────────────────────────────────────── dims ┐ ↓ draw, → chain ├─────────────────────────────────────────────────────────── layers ┤ :energy eltype: Float64 dims: draw, chain size: 1000×4 :n_steps eltype: Int64 dims: draw, chain size: 1000×4 :diverging eltype: Bool dims: draw, chain size: 1000×4 :max_energy_error eltype: Float64 dims: draw, chain size: 1000×4 :loglikelihood eltype: Float64 dims: draw, chain size: 1000×4 :energy_error eltype: Float64 dims: draw, chain size: 1000×4 :is_accept eltype: Bool dims: draw, chain size: 1000×4 :logprior eltype: Float64 dims: draw, chain size: 1000×4 :log_density eltype: Float64 dims: draw, chain size: 1000×4 :tree_depth eltype: Int64 dims: draw, chain size: 1000×4 :step_size eltype: Float64 dims: draw, chain size: 1000×4 :acceptance_rate eltype: Float64 dims: draw, chain size: 1000×4 :lp eltype: Float64 dims: draw, chain size: 1000×4 :step_size_nom eltype: Float64 dims: draw, chain size: 1000×4 ├───────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 2 entries: "created_at" => "2025-08-19T09:39:52.832" "inference_library" => "Turing"
Each group is a Dataset, a DimensionalData.AbstractDimStack that can be used identically to a DimensionalData.Dimstack. We can view a summary of the dataset.
idata_turing_post.posterior┌ 1000×4×8 Dataset ┐
├──────────────────┴──────────────────────────────────────────── dims ┐
↓ draw,
→ chain,
↗ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered
├───────────────────────────────────────────────────────────── layers ┤
:μ eltype: Float64 dims: draw, chain size: 1000×4
:τ eltype: Float64 dims: draw, chain size: 1000×4
:θ eltype: Float64 dims: draw, chain, school size: 1000×4×8
├─────────────────────────────────────────────────────────── metadata ┤
Dict{String, Any} with 2 entries:
"created_at" => "2025-08-19T09:39:52.91"
"inference_library" => "Turing"Here is a plot of the trace. Note the intelligent labels.
plot_trace(idata_turing_post);We can also generate summary stats…
summarystats(idata_turing_post)[TABLE]
SummaryStats
…and examine the energy distribution of the Hamiltonian sampler.
plot_energy(idata_turing_post);Additional information in Turing.jl
With a few more steps, we can use Turing to compute additional useful groups to add to the InferenceData.
To sample from the prior, one simply calls sample but with the Prior sampler:
prior = Turing.sample(rng2, param_mod_turing, Prior(), ndraws);Sampling 0%| | ETA: N/A
Sampling 0%|▎ | ETA: 0:01:26
Sampling 1%|▍ | ETA: 0:00:43
Sampling 2%|▋ | ETA: 0:00:28
Sampling 2%|▉ | ETA: 0:00:21
Sampling 2%|█ | ETA: 0:00:17
Sampling 3%|█▎ | ETA: 0:00:14
Sampling 4%|█▌ | ETA: 0:00:12
Sampling 4%|█▋ | ETA: 0:00:10
Sampling 4%|█▉ | ETA: 0:00:09
Sampling 5%|██▏ | ETA: 0:00:08
Sampling 6%|██▎ | ETA: 0:00:08
Sampling 6%|██▌ | ETA: 0:00:07
Sampling 6%|██▊ | ETA: 0:00:06
Sampling 7%|███ | ETA: 0:00:06
Sampling 8%|███▏ | ETA: 0:00:05
Sampling 8%|███▍ | ETA: 0:00:05
Sampling 8%|███▋ | ETA: 0:00:05
Sampling 9%|███▊ | ETA: 0:00:04
Sampling 10%|████ | ETA: 0:00:04
Sampling 10%|████▎ | ETA: 0:00:04
Sampling 10%|████▍ | ETA: 0:00:04
Sampling 11%|████▋ | ETA: 0:00:04
Sampling 12%|████▉ | ETA: 0:00:03
Sampling 12%|█████ | ETA: 0:00:03
Sampling 12%|█████▎ | ETA: 0:00:03
Sampling 13%|█████▌ | ETA: 0:00:03
Sampling 14%|█████▋ | ETA: 0:00:03
Sampling 14%|█████▉ | ETA: 0:00:03
Sampling 14%|██████▏ | ETA: 0:00:03
Sampling 15%|██████▎ | ETA: 0:00:03
Sampling 16%|██████▌ | ETA: 0:00:02
Sampling 16%|██████▊ | ETA: 0:00:02
Sampling 16%|██████▉ | ETA: 0:00:02
Sampling 17%|███████▏ | ETA: 0:00:02
Sampling 18%|███████▍ | ETA: 0:00:02
Sampling 18%|███████▌ | ETA: 0:00:02
Sampling 18%|███████▊ | ETA: 0:00:02
Sampling 19%|████████ | ETA: 0:00:02
Sampling 20%|████████▎ | ETA: 0:00:02
Sampling 20%|████████▍ | ETA: 0:00:02
Sampling 20%|████████▋ | ETA: 0:00:02
Sampling 21%|████████▉ | ETA: 0:00:02
Sampling 22%|█████████ | ETA: 0:00:02
Sampling 22%|█████████▎ | ETA: 0:00:02
Sampling 22%|█████████▌ | ETA: 0:00:02
Sampling 23%|█████████▋ | ETA: 0:00:02
Sampling 24%|█████████▉ | ETA: 0:00:02
Sampling 24%|██████████▏ | ETA: 0:00:01
Sampling 24%|██████████▎ | ETA: 0:00:01
Sampling 25%|██████████▌ | ETA: 0:00:01
Sampling 26%|██████████▊ | ETA: 0:00:01
Sampling 26%|██████████▉ | ETA: 0:00:01
Sampling 26%|███████████▏ | ETA: 0:00:01
Sampling 27%|███████████▍ | ETA: 0:00:01
Sampling 28%|███████████▌ | ETA: 0:00:01
Sampling 28%|███████████▊ | ETA: 0:00:01
Sampling 28%|████████████ | ETA: 0:00:01
Sampling 29%|████████████▏ | ETA: 0:00:01
Sampling 30%|████████████▍ | ETA: 0:00:01
Sampling 30%|████████████▋ | ETA: 0:00:01
Sampling 30%|████████████▊ | ETA: 0:00:01
Sampling 31%|█████████████ | ETA: 0:00:01
Sampling 32%|█████████████▎ | ETA: 0:00:01
Sampling 32%|█████████████▌ | ETA: 0:00:01
Sampling 32%|█████████████▋ | ETA: 0:00:01
Sampling 33%|█████████████▉ | ETA: 0:00:01
Sampling 34%|██████████████▏ | ETA: 0:00:01
Sampling 34%|██████████████▎ | ETA: 0:00:01
Sampling 34%|██████████████▌ | ETA: 0:00:01
Sampling 35%|██████████████▊ | ETA: 0:00:01
Sampling 36%|██████████████▉ | ETA: 0:00:01
Sampling 36%|███████████████▏ | ETA: 0:00:01
Sampling 36%|███████████████▍ | ETA: 0:00:01
Sampling 37%|███████████████▌ | ETA: 0:00:01
Sampling 38%|███████████████▊ | ETA: 0:00:01
Sampling 38%|████████████████ | ETA: 0:00:01
Sampling 38%|████████████████▏ | ETA: 0:00:01
Sampling 39%|████████████████▍ | ETA: 0:00:01
Sampling 40%|████████████████▋ | ETA: 0:00:01
Sampling 40%|████████████████▊ | ETA: 0:00:01
Sampling 40%|█████████████████ | ETA: 0:00:01
Sampling 41%|█████████████████▎ | ETA: 0:00:01
Sampling 42%|█████████████████▍ | ETA: 0:00:01
Sampling 42%|█████████████████▋ | ETA: 0:00:01
Sampling 42%|█████████████████▉ | ETA: 0:00:01
Sampling 43%|██████████████████ | ETA: 0:00:01
Sampling 44%|██████████████████▎ | ETA: 0:00:01
Sampling 44%|██████████████████▌ | ETA: 0:00:01
Sampling 44%|██████████████████▊ | ETA: 0:00:01
Sampling 45%|██████████████████▉ | ETA: 0:00:01
Sampling 46%|███████████████████▏ | ETA: 0:00:01
Sampling 46%|███████████████████▍ | ETA: 0:00:01
Sampling 46%|███████████████████▌ | ETA: 0:00:01
Sampling 47%|███████████████████▊ | ETA: 0:00:01
Sampling 48%|████████████████████ | ETA: 0:00:01
Sampling 48%|████████████████████▏ | ETA: 0:00:01
Sampling 48%|████████████████████▍ | ETA: 0:00:01
Sampling 49%|████████████████████▋ | ETA: 0:00:01
Sampling 50%|████████████████████▊ | ETA: 0:00:01
Sampling 50%|█████████████████████ | ETA: 0:00:00
Sampling 50%|█████████████████████▎ | ETA: 0:00:00
Sampling 51%|█████████████████████▍ | ETA: 0:00:00
Sampling 52%|█████████████████████▋ | ETA: 0:00:00
Sampling 52%|█████████████████████▉ | ETA: 0:00:00
Sampling 52%|██████████████████████ | ETA: 0:00:00
Sampling 53%|██████████████████████▎ | ETA: 0:00:00
Sampling 54%|██████████████████████▌ | ETA: 0:00:00
Sampling 54%|██████████████████████▋ | ETA: 0:00:00
Sampling 55%|██████████████████████▉ | ETA: 0:00:00
Sampling 55%|███████████████████████▏ | ETA: 0:00:00
Sampling 56%|███████████████████████▎ | ETA: 0:00:00
Sampling 56%|███████████████████████▌ | ETA: 0:00:00
Sampling 56%|███████████████████████▊ | ETA: 0:00:00
Sampling 57%|████████████████████████ | ETA: 0:00:00
Sampling 57%|████████████████████████▏ | ETA: 0:00:00
Sampling 58%|████████████████████████▍ | ETA: 0:00:00
Sampling 58%|████████████████████████▋ | ETA: 0:00:00
Sampling 59%|████████████████████████▊ | ETA: 0:00:00
Sampling 60%|█████████████████████████ | ETA: 0:00:00
Sampling 60%|█████████████████████████▎ | ETA: 0:00:00
Sampling 60%|█████████████████████████▍ | ETA: 0:00:00
Sampling 61%|█████████████████████████▋ | ETA: 0:00:00
Sampling 62%|█████████████████████████▉ | ETA: 0:00:00
Sampling 62%|██████████████████████████ | ETA: 0:00:00
Sampling 62%|██████████████████████████▎ | ETA: 0:00:00
Sampling 63%|██████████████████████████▌ | ETA: 0:00:00
Sampling 64%|██████████████████████████▋ | ETA: 0:00:00
Sampling 64%|██████████████████████████▉ | ETA: 0:00:00
Sampling 64%|███████████████████████████▏ | ETA: 0:00:00
Sampling 65%|███████████████████████████▎ | ETA: 0:00:00
Sampling 66%|███████████████████████████▌ | ETA: 0:00:00
Sampling 66%|███████████████████████████▊ | ETA: 0:00:00
Sampling 66%|███████████████████████████▉ | ETA: 0:00:00
Sampling 67%|████████████████████████████▏ | ETA: 0:00:00
Sampling 68%|████████████████████████████▍ | ETA: 0:00:00
Sampling 68%|████████████████████████████▌ | ETA: 0:00:00
Sampling 68%|████████████████████████████▊ | ETA: 0:00:00
Sampling 69%|█████████████████████████████ | ETA: 0:00:00
Sampling 70%|█████████████████████████████▎ | ETA: 0:00:00
Sampling 70%|█████████████████████████████▍ | ETA: 0:00:00
Sampling 70%|█████████████████████████████▋ | ETA: 0:00:00
Sampling 71%|█████████████████████████████▉ | ETA: 0:00:00
Sampling 72%|██████████████████████████████ | ETA: 0:00:00
Sampling 72%|██████████████████████████████▎ | ETA: 0:00:00
Sampling 72%|██████████████████████████████▌ | ETA: 0:00:00
Sampling 73%|██████████████████████████████▋ | ETA: 0:00:00
Sampling 74%|██████████████████████████████▉ | ETA: 0:00:00
Sampling 74%|███████████████████████████████▏ | ETA: 0:00:00
Sampling 74%|███████████████████████████████▎ | ETA: 0:00:00
Sampling 75%|███████████████████████████████▌ | ETA: 0:00:00
Sampling 76%|███████████████████████████████▊ | ETA: 0:00:00
Sampling 76%|███████████████████████████████▉ | ETA: 0:00:00
Sampling 76%|████████████████████████████████▏ | ETA: 0:00:00
Sampling 77%|████████████████████████████████▍ | ETA: 0:00:00
Sampling 78%|████████████████████████████████▌ | ETA: 0:00:00
Sampling 78%|████████████████████████████████▊ | ETA: 0:00:00
Sampling 78%|█████████████████████████████████ | ETA: 0:00:00
Sampling 79%|█████████████████████████████████▏ | ETA: 0:00:00
Sampling 80%|█████████████████████████████████▍ | ETA: 0:00:00
Sampling 80%|█████████████████████████████████▋ | ETA: 0:00:00
Sampling 80%|█████████████████████████████████▊ | ETA: 0:00:00
Sampling 81%|██████████████████████████████████ | ETA: 0:00:00
Sampling 82%|██████████████████████████████████▎ | ETA: 0:00:00
Sampling 82%|██████████████████████████████████▌ | ETA: 0:00:00
Sampling 82%|██████████████████████████████████▋ | ETA: 0:00:00
Sampling 83%|██████████████████████████████████▉ | ETA: 0:00:00
Sampling 84%|███████████████████████████████████▏ | ETA: 0:00:00
Sampling 84%|███████████████████████████████████▎ | ETA: 0:00:00
Sampling 84%|███████████████████████████████████▌ | ETA: 0:00:00
Sampling 85%|███████████████████████████████████▊ | ETA: 0:00:00
Sampling 86%|███████████████████████████████████▉ | ETA: 0:00:00
Sampling 86%|████████████████████████████████████▏ | ETA: 0:00:00
Sampling 86%|████████████████████████████████████▍ | ETA: 0:00:00
Sampling 87%|████████████████████████████████████▌ | ETA: 0:00:00
Sampling 88%|████████████████████████████████████▊ | ETA: 0:00:00
Sampling 88%|█████████████████████████████████████ | ETA: 0:00:00
Sampling 88%|█████████████████████████████████████▏ | ETA: 0:00:00
Sampling 89%|█████████████████████████████████████▍ | ETA: 0:00:00
Sampling 90%|█████████████████████████████████████▋ | ETA: 0:00:00
Sampling 90%|█████████████████████████████████████▊ | ETA: 0:00:00
Sampling 90%|██████████████████████████████████████ | ETA: 0:00:00
Sampling 91%|██████████████████████████████████████▎ | ETA: 0:00:00
Sampling 92%|██████████████████████████████████████▍ | ETA: 0:00:00
Sampling 92%|██████████████████████████████████████▋ | ETA: 0:00:00
Sampling 92%|██████████████████████████████████████▉ | ETA: 0:00:00
Sampling 93%|███████████████████████████████████████ | ETA: 0:00:00
Sampling 94%|███████████████████████████████████████▎ | ETA: 0:00:00
Sampling 94%|███████████████████████████████████████▌ | ETA: 0:00:00
Sampling 94%|███████████████████████████████████████▊ | ETA: 0:00:00
Sampling 95%|███████████████████████████████████████▉ | ETA: 0:00:00
Sampling 96%|████████████████████████████████████████▏ | ETA: 0:00:00
Sampling 96%|████████████████████████████████████████▍ | ETA: 0:00:00
Sampling 96%|████████████████████████████████████████▌ | ETA: 0:00:00
Sampling 97%|████████████████████████████████████████▊ | ETA: 0:00:00
Sampling 98%|█████████████████████████████████████████ | ETA: 0:00:00
Sampling 98%|█████████████████████████████████████████▏| ETA: 0:00:00
Sampling 98%|█████████████████████████████████████████▍| ETA: 0:00:00
Sampling 99%|█████████████████████████████████████████▋| ETA: 0:00:00
Sampling 100%|█████████████████████████████████████████▊| ETA: 0:00:00
Sampling 100%|██████████████████████████████████████████| Time: 0:00:00
Sampling 100%|██████████████████████████████████████████| Time: 0:00:00To draw from the prior and posterior predictive distributions we can instantiate a “predictive model”, i.e. a Turing model but with the observations set to missing, and then calling predict on the predictive model and the previously drawn samples:
# Instantiate the predictive model
param_mod_predict = model_turing(similar(y, Missing), σ)
# and then sample!
prior_predictive = Turing.predict(rng2, param_mod_predict, prior)
posterior_predictive = Turing.predict(rng2, param_mod_predict, turing_chns);And to extract the pointwise log-likelihoods, which is useful if you want to compute metrics such as loo,
log_likelihood = let
log_likelihood = Turing.pointwise_loglikelihoods(
param_mod_turing, MCMCChains.get_sections(turing_chns, :parameters)
)
# Ensure the ordering of the loglikelihoods matches the ordering of `posterior_predictive`
ynames = string.(keys(posterior_predictive))
log_likelihood_y = getindex.(Ref(log_likelihood), ynames)
(; y=cat(log_likelihood_y...; dims=3))
end;This can then be included in the from_mcmcchains call from above:
idata_turing = from_mcmcchains(
turing_chns;
posterior_predictive,
log_likelihood,
prior,
prior_predictive,
observed_data=(; y),
coords=(; school=schools),
dims=NamedTuple(k => (:school,) for k in (:y, :σ, :θ)),
library=Turing,
)InferenceData
posterior
┌ 1000×4×8 Dataset ┐ ├──────────────────┴──────────────────────────────────────────── dims ┐ ↓ draw, → chain, ↗ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered ├───────────────────────────────────────────────────────────── layers ┤ :μ eltype: Float64 dims: draw, chain size: 1000×4 :τ eltype: Float64 dims: draw, chain size: 1000×4 :θ eltype: Float64 dims: draw, chain, school size: 1000×4×8 ├─────────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 3 entries: "created_at" => "2025-08-19T09:40:24.737" "inference_library_version" => "0.40.2" "inference_library" => "Turing"
posterior_predictive
┌ 1000×4×8 Dataset ┐ ├──────────────────┴──────────────────────────────────────────── dims ┐ ↓ draw, → chain, ↗ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered ├───────────────────────────────────────────────────────────── layers ┤ :y eltype: Float64 dims: draw, chain, school size: 1000×4×8 ├─────────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 3 entries: "created_at" => "2025-08-19T09:40:24.274" "inference_library_version" => "0.40.2" "inference_library" => "Turing"
log_likelihood
┌ 1000×4×8 Dataset ┐ ├──────────────────┴──────────────────────────────────────────── dims ┐ ↓ draw, → chain, ↗ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered ├───────────────────────────────────────────────────────────── layers ┤ :y eltype: Float64 dims: draw, chain, school size: 1000×4×8 ├─────────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 3 entries: "created_at" => "2025-08-19T09:40:24.577" "inference_library_version" => "0.40.2" "inference_library" => "Turing"
sample_stats
┌ 1000×4 Dataset ┐ ├────────────────┴──────────────────────────────────────────── dims ┐ ↓ draw, → chain ├─────────────────────────────────────────────────────────── layers ┤ :energy eltype: Float64 dims: draw, chain size: 1000×4 :n_steps eltype: Int64 dims: draw, chain size: 1000×4 :diverging eltype: Bool dims: draw, chain size: 1000×4 :max_energy_error eltype: Float64 dims: draw, chain size: 1000×4 :loglikelihood eltype: Float64 dims: draw, chain size: 1000×4 :energy_error eltype: Float64 dims: draw, chain size: 1000×4 :is_accept eltype: Bool dims: draw, chain size: 1000×4 :logprior eltype: Float64 dims: draw, chain size: 1000×4 :log_density eltype: Float64 dims: draw, chain size: 1000×4 :tree_depth eltype: Int64 dims: draw, chain size: 1000×4 :step_size eltype: Float64 dims: draw, chain size: 1000×4 :acceptance_rate eltype: Float64 dims: draw, chain size: 1000×4 :lp eltype: Float64 dims: draw, chain size: 1000×4 :step_size_nom eltype: Float64 dims: draw, chain size: 1000×4 ├───────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 3 entries: "created_at" => "2025-08-19T09:40:24.737" "inference_library_version" => "0.40.2" "inference_library" => "Turing"
prior
┌ 1000×1×8 Dataset ┐ ├──────────────────┴──────────────────────────────────────────── dims ┐ ↓ draw, → chain, ↗ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered ├───────────────────────────────────────────────────────────── layers ┤ :μ eltype: Float64 dims: draw, chain size: 1000×1 :τ eltype: Float64 dims: draw, chain size: 1000×1 :θ eltype: Float64 dims: draw, chain, school size: 1000×1×8 ├─────────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 3 entries: "created_at" => "2025-08-19T09:40:25.306" "inference_library_version" => "0.40.2" "inference_library" => "Turing"
prior_predictive
┌ 1000×1×8 Dataset ┐ ├──────────────────┴──────────────────────────────────────────── dims ┐ ↓ draw, → chain, ↗ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered ├───────────────────────────────────────────────────────────── layers ┤ :y eltype: Float64 dims: draw, chain, school size: 1000×1×8 ├─────────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 3 entries: "created_at" => "2025-08-19T09:40:25.138" "inference_library_version" => "0.40.2" "inference_library" => "Turing"
sample_stats_prior
┌ 1000×1 Dataset ┐ ├────────────────┴───────────────────────────────────────── dims ┐ ↓ draw, → chain ├──────────────────────────────────────────────────────── layers ┤ :logprior eltype: Float64 dims: draw, chain size: 1000×1 :lp eltype: Float64 dims: draw, chain size: 1000×1 :loglikelihood eltype: Float64 dims: draw, chain size: 1000×1 ├────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 3 entries: "created_at" => "2025-08-19T09:40:25.233" "inference_library_version" => "0.40.2" "inference_library" => "Turing"
observed_data
┌ 8-element Dataset ┐ ├───────────────────┴──────────────────────────────────────────── dims ┐ ↓ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered ├────────────────────────────────────────────────────────────── layers ┤ :y eltype: Float64 dims: school size: 8 ├──────────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 3 entries: "created_at" => "2025-08-19T09:40:25.503" "inference_library_version" => "0.40.2" "inference_library" => "Turing"
Then we can for example compute the expected leave-one-out (LOO) predictive density, which is an estimate of the out-of-distribution predictive fit of the model:
loo(idata_turing) # higher ELPD is betterPSISLOOResult with estimates
elpd elpd_mcse p p_mcse
-31 1.4 0.9 0.33
and PSISResult with 1000 draws, 4 chains, and 8 parameters
Pareto shape (k) diagnostic values:
Count Min. ESS
(-Inf, 0.5] good 6 (75.0%) 313
(0.5, 0.7] okay 2 (25.0%) 1049If the model is well-calibrated, i.e. it replicates the true generative process well, the CDF of the pointwise LOO values should be similarly distributed to a uniform distribution. This can be inspected visually:
plot_loo_pit(idata_turing; y=:y, ecdf=true);Plotting with Stan.jl outputs
StanSample.jl comes with built-in support for producing InferenceData outputs.
Here is the same centered eight schools model in Stan:
schools_code = """
data {
int<lower=0> J;
array[J] real y;
array[J] real<lower=0> sigma;
}
parameters {
real mu;
real<lower=0> tau;
array[J] real theta;
}
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_data = Dict("J" => J, "y" => y, "sigma" => σ)
idata_stan = mktempdir() do path
stan_model = SampleModel("schools", schools_code, path)
_ = stan_sample(
stan_model;
data=schools_data,
num_chains=nchains,
num_warmups=ndraws_warmup,
num_samples=ndraws,
seed=28983,
summary=false,
)
return StanSample.inferencedata(
stan_model;
posterior_predictive_var=:y_hat,
observed_data=(; y),
log_likelihood_var=:log_lik,
coords=(; school=schools),
dims=NamedTuple(
k => (:school,) for k in (:y, :sigma, :theta, :log_lik, :y_hat)
),
)
end[ Info: /tmp/jl_q9qkTM/schools.stan updated.InferenceData
posterior
┌ 1000×4×8 Dataset ┐ ├──────────────────┴──────────────────────────────────────────── dims ┐ ↓ draw, → chain, ↗ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered ├───────────────────────────────────────────────────────────── layers ┤ :mu eltype: Float64 dims: draw, chain size: 1000×4 :tau eltype: Float64 dims: draw, chain size: 1000×4 :theta eltype: Float64 dims: draw, chain, school size: 1000×4×8 ├─────────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 1 entry: "created_at" => "2025-08-19T09:41:06.675"
posterior_predictive
┌ 1000×4×8 Dataset ┐ ├──────────────────┴──────────────────────────────────────────── dims ┐ ↓ draw, → chain, ↗ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered ├───────────────────────────────────────────────────────────── layers ┤ :y_hat eltype: Float64 dims: draw, chain, school size: 1000×4×8 ├─────────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 1 entry: "created_at" => "2025-08-19T09:41:06.262"
log_likelihood
┌ 1000×4×8 Dataset ┐ ├──────────────────┴──────────────────────────────────────────── dims ┐ ↓ draw, → chain, ↗ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered ├───────────────────────────────────────────────────────────── layers ┤ :log_lik eltype: Float64 dims: draw, chain, school size: 1000×4×8 ├─────────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 1 entry: "created_at" => "2025-08-19T09:41:06.584"
sample_stats
┌ 1000×4 Dataset ┐ ├────────────────┴─────────────────────────────────────────── dims ┐ ↓ draw, → chain ├────────────────────────────────────────────────────────── layers ┤ :tree_depth eltype: Int64 dims: draw, chain size: 1000×4 :energy eltype: Float64 dims: draw, chain size: 1000×4 :diverging eltype: Bool dims: draw, chain size: 1000×4 :acceptance_rate eltype: Float64 dims: draw, chain size: 1000×4 :n_steps eltype: Int64 dims: draw, chain size: 1000×4 :lp eltype: Float64 dims: draw, chain size: 1000×4 :step_size eltype: Float64 dims: draw, chain size: 1000×4 ├──────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 1 entry: "created_at" => "2025-08-19T09:41:06.401"
observed_data
┌ 8-element Dataset ┐ ├───────────────────┴──────────────────────────────────────────── dims ┐ ↓ school Categorical{String} ["Choate", …, "Mt. Hermon"] Unordered ├────────────────────────────────────────────────────────────── layers ┤ :y eltype: Float64 dims: school size: 8 ├──────────────────────────────────────────────────────────── metadata ┤ Dict{String, Any} with 1 entry: "created_at" => "2025-08-19T09:41:06.731"
plot_density(idata_stan; var_names=(:mu, :tau));Here is a plot showing where the Hamiltonian sampler had divergences:
plot_pair(
idata_stan;
coords=Dict(:school => ["Choate", "Deerfield", "Phillips Andover"]),
divergences=true,
);Environment
using Pkg
Pkg.status()Status `~/work/ArviZ.jl/ArviZ.jl/docs/Project.toml`
⌃ [cbdf2221] AlgebraOfGraphics v0.11.4
[131c737c] ArviZ v0.12.3 `~/work/ArviZ.jl/ArviZ.jl`
[2f96bb34] ArviZExampleData v0.2.0
[4a6e88f0] ArviZPythonPlots v0.1.9
[13f3f980] CairoMakie v0.15.6
[a93c6f00] DataFrames v1.7.0
[0703355e] DimensionalData v0.29.23
[31c24e10] Distributions v0.25.120
[e30172f5] Documenter v1.14.1
[f6006082] EvoTrees v0.17.4
[b5cf5a8d] InferenceObjects v0.4.12
[be115224] MCMCDiagnosticTools v0.3.15
[a7f614a8] MLJBase v1.8.2
[614be32b] MLJIteration v0.6.3
[ce719bf2] PSIS v0.9.8
[7f36be82] PosteriorStats v0.2.8
[c1514b29] StanSample v7.10.2
[a19d573c] StatisticalMeasures v0.2.1
[10745b16] Statistics v1.11.1
[2913bbd2] StatsBase v0.34.6
[fce5fe82] Turing v0.40.2
[f43a241f] Downloads v1.6.0
[37e2e46d] LinearAlgebra v1.11.0
Info Packages marked with ⌃ have new versions available and may be upgradable.versioninfo()Julia Version 1.11.6
Commit 9615af0f269 (2025-07-09 12:58 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 4 × AMD EPYC 7763 64-Core Processor
WORD_SIZE: 64
LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 2 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
JULIA_PROJECT = @.
JULIA_NUM_THREADS = 2
JULIA_LOAD_PATH = @:@stdlib
JULIA_PYTHONCALL_EXE = /home/runner/work/ArviZ.jl/ArviZ.jl/docs/.CondaPkg/.pixi/envs/default/bin/python