Visual Predictive Checks

Use this skill when running prior or posterior predictive checks to validate Bayesian models. These checks compare simulated data from the model to observed data (or plausible ranges for prior predictive checks).

ArviZ Workflow

1. Fit model with CmdStanPy, generating predictive quantities in generated quantities block (e.g., y_rep for posterior predictive, y_prior_pred for prior predictive)
2. Convert to ArviZ DataTree using arviz_base.from_cmdstanpy, specifying predictive groups
3. Create visual checks using arviz_plots functions

Visual Checks by Data Type

Continuous Data

• Distribution: plot_ppc_dist with kind="ecdf" and kind="kde"
• PIT ECDF: plot_ppc_pit - shows calibration with simultaneous bands
• Coverage: plot_ppc_pit(coverage=True) - equal-tailed interval coverage
• Summary statistics: plot_ppc_tstat for median, MAD, IQR combined with combine_plots
• LOO-PIT: plot_loo_pit - avoids double-dipping by using leave-one-out

Count Data

• Rootogram: plot_ppc_rootogram - emphasizes discreteness and dispersion
• Histogram: plot_ppc_dist(kind="hist")
• PIT ECDF and coverage: Same as continuous

Binary/Categorical/Ordinal Data

• Calibration: plot_ppc_pava - PAV-adjusted calibration curves
• Intervals: plot_ppc_interval - posterior predictive intervals with observed overlay
• PIT ECDF and coverage: Same as continuous

Censored/Survival Data

• Survival curves: plot_ppc_censored - Kaplan-Meier style PPC
• PIT ECDF and coverage: Same as continuous

Key Principles

Use multiple complementary views rather than relying on a single plot. For example, for continuous outcomes, combine ECDF (shows full distribution) with PIT ECDF (shows calibration) and t-stat PPCs (shows specific features like central tendency and spread).

LOO-PIT is preferred over regular PIT for posterior checks as it approximates leave-one-out predictive distribution and avoids overfitting concerns.

Name plots descriptively: prior_predictive_ecdf.png, loo_pit_calibration.png, posterior_rootogram.png.