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\noindent Statistica Sinica {\bf 13}(2003), 423-442
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\centerline{\large\bf A BAYESIAN APPROACH TO THE SELECTION AND}
\vspace{2pt}
\centerline{\large\bf TESTING OF MIXTURE MODELS}
\vspace{.25cm}
\centerline{Johannes Berkhof, Iven van Mechelen and Andrew Gelman}
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\centerline{\it
Catholic University Leuven,
Free University Medical Center}
\centerline{\it and
Columbia University}
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\begin{quotation}
\noindent {\it Abstract:}
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.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Bayes factor, non-identifiability, hyperprior, latent class model,
posterior predictive check, prior sensitivity, psychiatric diagnosis.\par
\end{quotation}
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