Penalized loss functions for Bayesian model comparison

Biostatistics. 2008 Jul;9(3):523-39. doi: 10.1093/biostatistics/kxm049. Epub 2008 Jan 21.


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.

MeSH terms

  • Acetylation
  • Arylamine N-Acetyltransferase / genetics
  • Arylamine N-Acetyltransferase / metabolism
  • Bayes Theorem*
  • Bias
  • Biometry / methods
  • Cohort Studies
  • Confidence Intervals
  • Decision Theory*
  • Factor Analysis, Statistical
  • Forecasting
  • Humans
  • Lip Neoplasms / epidemiology
  • Male
  • Markov Chains
  • Models, Biological*
  • Models, Statistical*
  • Monte Carlo Method
  • Rare Diseases / epidemiology
  • Reference Values
  • Regression Analysis
  • Research Design / statistics & numerical data*
  • Scotland


  • Arylamine N-Acetyltransferase
  • NAT2 protein, human