Posterior predictive check

A posterior predictive check is a Bayesian diagnostic in which simulated data from the fitted model are compared to observed data to assess model adequacy. Unlike Bayesian model comparison, which asks which model is more probable, posterior predictive checking asks whether any model is adequate. It is a practical alternative when the marginal likelihood is intractable. The technique is closely related to predictive model checking and shares goals with non-Bayesian methods like cross-validation.