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Posterior predictive check — how do you use it?

hard

Answer

  • Simulate replicated datasets yrepy_{\mathrm{rep}} from posterior predictive; compare their summary statistics (mean, quantiles, distribution shape) to observed data.
  • If observed data looks like a plausible draw from yrepy_{\mathrm{rep}}, the model captures the data — otherwise, refine.
  • Formalized via Bayesian p-values: fraction of yrepy_{\mathrm{rep}} with statistic ≥ observed.
  • Standard diagnostic step in ArviZ, brms, Stan.
Check yourself — multiple choice
  • Random
  • Simulate yrepy_{\mathrm{rep}} from posterior predictive, compare summaries to observed data → refine model if mismatch; Bayesian p-value formalizes it
  • Same as prior predictive
  • Not real

Posterior predictive check: compare yrepy_{\mathrm{rep}} summaries to observed; refine model.

#bayesian

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