A Bayesian approach to the selection and testing of mixture models

Johannes Berkhof*, Iven Van Mechelen, Andrew Gelman

*Corresponding author for this work

Research output: Contribution to journalReview articleAcademicpeer-review


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.

Original languageEnglish
Pages (from-to)423-442
Number of pages20
JournalStatistica Sinica
Issue number2
Publication statusPublished - Apr 2003

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