Useful model checking tools can be constructed by measuring the distance between a prior distribution that concentrates most of its mass around a model of interest, and the resulting posterior distribution. In this paper we use this approach to construct a diagnostic measure for detecting lack of fit in discrete data, with special focus on binomial data. We begin by constructing a suitable probability model “around” the model of interest, via a Dirichlet Process elaboration. We derive the resulting diagnostic and show that, approximately, it is the sum of two terms: the first is the logarithm of the Bayes factor and the second is proportional to the Pearson chi-square statistics. We give details of a simulation algorithm for computing the diagnostic and illustrate its use in an application to biomedical data.
A Dirichlet process elaboration diagnostic for binomial goodness of fit
CAROTA, Cinzia;
1998-01-01
Abstract
Useful model checking tools can be constructed by measuring the distance between a prior distribution that concentrates most of its mass around a model of interest, and the resulting posterior distribution. In this paper we use this approach to construct a diagnostic measure for detecting lack of fit in discrete data, with special focus on binomial data. We begin by constructing a suitable probability model “around” the model of interest, via a Dirichlet Process elaboration. We derive the resulting diagnostic and show that, approximately, it is the sum of two terms: the first is the logarithm of the Bayes factor and the second is proportional to the Pearson chi-square statistics. We give details of a simulation algorithm for computing the diagnostic and illustrate its use in an application to biomedical data.
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