Journal
BIOSTATISTICS
Volume 9, Issue 3, Pages 523-539Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biostatistics/kxm049
Keywords
Bayesian model comparison; deviance information criterion; disease mapping; Markov chain Monte Carlo methods; mixture models
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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.
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