Penalized loss functions for Bayesian model comparison.
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.
Plummer
Martyn
M
International Agency for Research on Cancer, 150 Cours Albert Thomas, 69372 Lyon Cedex 08, France. plummer@iarc.fr
D000107:Acetylation; D001191:Arylamine N-Acetyltransferase / Q000235:genetics / Q000378:metabolism; D001499:Bayes Theorem; D015982:Bias; D001699:Biometry / Q000379:methods; D015331:Cohort Studies; D016001:Confidence Intervals; D003662:Decision Theory; D005163:Factor Analysis, Statistical; D005544:Forecasting; D006801:Humans; D008048:Lip Neoplasms / Q000453:epidemiology; D008297:Male; D008390:Markov Chains; D008954:Models, Biological; D015233:Models, Statistical; D009010:Monte Carlo Method; D035583:Rare Diseases / Q000453:epidemiology; D012016:Reference Values; D012044:Regression Analysis; D012107:Research Design / Q000706:statistics & numerical data*; D012606:Scotland
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