Predictive Bayesian Model Selection

SYNOPTIC ABSTRACT

We investigate the problem of evaluating the goodness of the predictive distributions of Bayesian models. Recently, deviance information criteria (DIC) has been extensively employed in various study areas to evaluate the Bayesian models, thanks to its simplicity of calculation from the posterior simulation outputs. Unfortunately, it is known that DIC often selects overfitted models. In this paper, we develop a new criterion which can be calculated easily from posterior outputs under the model misspecification situation. The proposed criterion is developed as an estimator of the posterior mean of the expected likelihood and is robust to improper priors. Monte Carlo simulations are conducted to investigate the properties of the proposed criteria.

Key words and Phrases:

• Effective number of parameters
• Empirical Bayes Markov chain Monte Carlo
• Model misspecification
• Hierarchical Bayesian model