PyMC Bayesian Modeling

Version and scope

Targets PyMC 6.3.2, PyTensor 3.3.2, and ArviZ 1.3.0. These are local Python APIs, with no service endpoint, credentials, or remote inference required. The native tests use the PyMC NUTS sampler on small synthetic models. Optional nutpie/JAX samplers, SMC, and production-scale convergence are not validated by those tests. Record the complete resolved environment, backend, seeds, preprocessing, and data provenance for a scientific run.

Local macOS validation used PYTENSOR_FLAGS="cxx=" after the C linker failed with library 'd64' not found; this disables PyTensor C compilation for that process. The Python library workflows passed under that setting; it does not establish that the C backend works on this host.

ArviZ 1 splits into base/stats/plots packages, re-exported by import arviz as az. PyMC returns an xarray DataTree despite the legacy return_inferencedata option name. az.summary(..., round_to="none") returns numerical columns; the default formats for display. Use az.plot_ppc_dist, az.plot_dist, and az.plot_trace_dist; save their returned PlotCollection, not a separate pyplot figure. az.hdi(..., prob=.95) uses prob, with bounds along ci_bound.

Workflow

1. Define the estimand and predictive unit: another measurement, a new patient or group, or a future time block. Preserve units, missingness assumptions and grouping. Fit any scaling only on training data; reject constant columns.
2. Build a generative model with scientifically calibrated priors and named dimensions. Check likelihood support, finite initial log probability, design rank, confounding and symmetries before sampling.
3. Run a prior predictive check and inspect domain-relevant summaries before fitting. A broad prior is not automatically noninformative or plausible.
4. Fit several independent chains with explicit seeds. For reproducible backend selection use nuts_sampler="pymc"; the automatic choice can prefer installed nutpie. nuts={...} replaces deprecated nuts_sampler_kwargs.
5. Inspect rank R-hat, bulk/tail ESS, estimand-specific MCSE, divergences, energy BFMI and sampler-specific tree depth. Fix geometry and initialization before simply increasing draws. A clean screen does not prove convergence.
6. Generate posterior predictive replicates and inspect residual structure, tails, zeros, group effects and time dependence relevant to the question. In-sample agreement is not external validation or parameter identifiability.
7. Compare prior sensitivity and parameter recovery on synthetic data. Weakly informed scales, correlated parameters, separated logistic data, or mixture label switching can survive good MCMC diagnostics. A proper prior may make a posterior finite without the likelihood identifying its parameters.
8. Predict using the correct training transform and uncertainty levels. Keep predictions separate from in-sample posterior_predictive. Restore model data before recomputing training likelihoods.

See standard_workflow.md for a complete bounded API smoke example, workflows.md for missing values, scaling, predictive scoring and serialization, and model_patterns.md for model structures.

Runnable templates

From the skill directory, run the synthetic linear or hierarchical template:

uv run --isolated --with "pymc==6.3.2" --with "arviz==1.3.0" --with "pytensor==3.3.2" --with matplotlib --with pandas --with h5netcdf --with h5py python assets/linear_regression_template.py --draws 80 --tune 80 --chains 2 --output-dir linear_smoke
uv run --isolated --with "pymc==6.3.2" --with "arviz==1.3.0" --with "pytensor==3.3.2" --with matplotlib --with pandas --with h5netcdf --with h5py python assets/hierarchical_model_template.py --draws 80 --tune 80 --chains 2 --output-dir hierarchical_smoke

These short commands intentionally test execution and artifacts; they are not adequate evidence of converged scientific estimates. For a real analysis, inspect priors before fitting and budget chains/draws around diagnostics and required MCSE. The templates default to four chains and longer runs, but those counts are not acceptance criteria by themselves.

The hierarchical template predicts an unseen group by drawing group effects from every hyperposterior draw, sharing each group effect across that group's new rows, then adding observation noise. Using only population means omits between-group uncertainty. Centered, non-centered, and partial parameterizations can each be appropriate; non-centering is not universally superior.

Diagnostic and comparison helpers

Import the modules from this skill's scripts/ directory (add that directory to sys.path when working elsewhere). Example fragments below assume fitted data:

from scripts.model_diagnostics import check_diagnostics, create_diagnostic_report
result = check_diagnostics(idata, var_names=["alpha", "beta", "sigma"])
create_diagnostic_report(idata, var_names=["alpha", "beta", "sigma"], output_dir="diagnostics")

check_diagnostics flags nonfinite statistics and insufficient chains. It reports missing HMC statistics as unavailable rather than claiming zero divergences. It uses recorded reached_max_treedepth, or an explicit max_treedepth matching the actual sampler; never infer the configured limit from the maximum observed value. The default ESS floor of 400 is pooled across chains, a screening floor, not a universal precision target. BFMI below 0.3 is a warning heuristic.

from scripts.model_comparison import compare_models, check_loo_reliability, model_averaging
models = {"linear": idata_linear, "robust": idata_robust}
check_loo_reliability(models, var_name="y_obs")
comparison = compare_models(models, var_name="y_obs")
mixture_draws, weights = model_averaging(models, var_name="y_obs", random_seed=42)

Compute pointwise log likelihood while the model contains the training data: pm.compute_log_likelihood(idata, model=model). Passing log_likelihood through idata_kwargs still works in 6.3.2 but now emits a deprecation warning. ArviZ 1 az.compare ranks PSIS-LOO ELPD and has no ic= argument. The helper retains ic="loo" as an explicit compatibility option. WAIC is separate and is not a remedy for failed PSIS diagnostics. Use each LOO result's good_k threshold, refit influential holdouts or choose structured cross-validation when needed.

Comparisons require identical outcomes, ordering, scale, likelihood measure and predictive unit. A higher ELPD is preferable for that target; inspect paired score uncertainty and diagnostics before ranking. Stacking weights are predictive combination weights, not posterior model probabilities.

Version 2 behavior change: model_averaging now samples a predictive mixture with shape (sample, *prediction_dimensions), preserving both within-model and between-model variation. It returns weights in input model order and rejects missing/misaligned predictions or invalid weights. Pointwise averages of paired posterior draws are not draws from a mixture. Use an explicit group="predictions" for new data; the default is posterior_predictive.

Distribution and inference choices

• Continuous outcomes: Normal or Student-t with scale calibrated to units.
• Counts: Poisson for equidispersion, NegativeBinomial for overdispersion; audit the zero-generating mechanism before adding a hurdle or zero-inflation term.
• Binary outcomes: Bernoulli with logit_p; priors must remain plausible on the probability scale, especially under separation.
• Positive scales: HalfNormal, Exponential or Gamma with domain-specific scales.
• Covariance: LKJCholeskyCov; ordinary dims labels do not align PyTensor math.
• VI: pm.fit provides approximations that can miss modes and underestimate uncertainty. Finite ELBO and good ESS on approximation draws do not establish posterior accuracy. Compare against MCMC on a feasible representative model.

See distributions.md for parameter conventions and sampling_inference.md for NUTS, discrete sampling, variational inference, prediction semantics and limitations.

Primary sources

Reviewed 2026-10-01: PyMC sampling, data containers, forward sampling source, ArviZ LOO, comparison, predictive plots.