Posterior Predictive Distribution

Abstract The posterior predictive distribution is the distribution of future observations, conditioned on the information available from existing observations. It is the main Bayesian tool for treating predictive problems in statistics. We define the posterior predictive distribution and illustrate its main features in Bayesian parametric inference. We also focus on predictive model checking and selection, which are procedures for checking model adequacy and for selecting a model, when the analysis is based on a posterior predictive approach.