A Bayesian approach to the selection and testing of mixture models

An important aspect of mixture modeling is the selection of the number of mixture components. In this paper, we discuss the Bayes factor as a selection tool. The discussion will focus on two aspects: computation of the Bayes factor and prior sensitivity. For the computation, we propose a variant of Chib's estimator that accounts for the non-identifiability of the mixture components. To reduce the prior sensitivity of the Bayes factor, we propose to extend the model with a hyperprior. We further discuss the use of posterior predictive checks for examining the fit of the model. The ideas are illustrated by means of a psychiatric diagnosis example.