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Biostatistics Advance Access published online on January 21, 2008
Biostatistics, doi:10.1093/biostatistics/kxm049
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Penalized loss functions for Bayesian model comparison

Martyn Plummer

International Agency for Research on Cancer, 150 Cours Albert Thomas, 69372 Lyon Cedex 08, France

plummer{at}iarc.fr

The deviance information criterion (DIC) is widely used for Bayesian model comparison, despite the lack of a clear theoretical foundation. DIC is shown to be an approximation to a penalized loss function based on the deviance, with a penalty derived from a cross-validation argument. This approximation is valid only when the effective number of parameters in the model is much smaller than the number of independent observations. In disease mapping, a typical application of DIC, this assumption does not hold and DIC under-penalizes more complex models. Another deviance-based loss function, derived from the same decision-theoretic framework, is applied to mixture models, which have previously been considered an unsuitable application for DIC

Keywords: Bayesian model comparison; Deviance information criterion; Disease mapping; Markov chain Monte Carlo methods; Mixture models

Received June 15, 2007; revised November 12, 2007; accepted for publication November 20, 2007.


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