MCMC convergence diagnostics using CmdStanPy and ArviZ
Runs MCMC convergence diagnostics on Stan models using CmdStanPy and ArviZ to verify chain mixing and effective sample size.
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Use this skill when checking MCMC convergence after fitting Stan models. Convergence means chains mixed and explored the same target, and you have enough effective draws.
After fitting with CmdStanPy, run:
fit.summary(): Returns DataFrame with R-hat, ESS_bulk, ESS_tail, MCSE per parameterfit.diagnose(): Checks for divergences, max treedepth, low E-BFMI, low ESS, high R-hatIf diagnose() reports no problems, you still need visual checks via ArviZ.
Convert to InferenceData:
idata = az.from_cmdstanpy(
fit,
log_likelihood="log_lik",
observed_data={"y": y_obs}
)
Run numerical diagnostics:
az.rhat(idata): Rank-normalized split R-hataz.ess(idata): Bulk and tail effective sample sizeaz.bfmi(idata): Bayesian fraction of missing informationaz.mcse(idata): Monte Carlo standard erroraz.summary(idata): All diagnostics in one tableMust achieve:
Chain mixing and stationarity:
az.plot_trace(): Should show "fat fuzzy caterpillars", no trends or stuck chains. Divergences shown as vertical lines.az.plot_rank(): Rank histograms should be uniform and similar across chains. U-shapes or skew indicate poor mixing.Autocorrelation and ESS:
az.plot_autocorr(): Slow decay indicates high correlation and low ESSaz.plot_ess(kind="evolution"): ESS growth over draws - should keep climbingaz.plot_ess(kind="local"): ESS in local windows/quantiles - checks tail explorationHMC-specific pathologies:
az.plot_energy(): Overlays energy transitions vs marginal energy. Low BFMI shows mismatch.az.plot_pair(divergences=True): Localizes divergences in parameter space (funnels, tight correlations)az.plot_parallel(): Parallel coordinates showing divergent vs non-divergent drawsRemember: You never prove convergence, only build a strong circumstantial case. The sampler tells you about your model - listen to it.
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