The posterior predictive p-value for the problem of goodness of fit

Abstract

The aim of this paper is to explore some features and possible uses of the posterior predictivep-value for the problem of goodness of fit. First, the behaviour of the posterior predictivep-value is compared with the behaviour of the classicalp-value through some interesting examples. Then, we consider a decision problem for simultaneously deciding to accept/reject a modelM and to accept/reject a null hypothesis (if we have accepted the modelM); the posterior predictivep-value is used for estimating the posterior probability of the model.[PUBLICATION ABSTRACT]