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Abstract:
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Various popular Bayesian model selection criteria, such as Log Pseudo Marginal Likelihood (LPML) based on the conditional predictive ordinates (CPO), are based on the general notion of one-deleted cross-validation. The Deviance Information Criterion (DIC) is another popular predictive model selection criterion. These criteria can often be estimated from Markov chain samples with reasonable ease. In this article, via extensive simulation studies for linear, logistic, and survival models, we show that, LPML and DIC have poor performance in selecting the data generating model. The poor performance persists even in the setting of large number of observations. We provide theoretical explanation of this poor performance in the context of linear regression models. We further find that the Highest Posterior Model (HPM) or highest marginal likelihood approach to Bayesian variable selection performs substantially better.
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