Deviance information criterion for Bayesian model selection: Justification and variation - LI, Yong (Institutional Knowledge at Singapore Management University, 2017)
Deviance information criterion (DIC) has been extensively used for making Bayesian model selection. It is a Bayesian version of AIC and chooses a model that gives the smallest expected Kullback-Leibler divergence between the data generating process (DGP) and a predictive distribution asymptotically. We show that when the plug-in predictive distribution is used, DIC can have a rigorous decision-theoretic justification under regularity conditions. An alternative expression for DIC, based on the Bayesian predictive distribution, is proposed. The new DIC has a smaller penalty term than the original DIC and is very easy to compute from the MCMC output. It is invariant to reparameterization and yields a smaller expected loss than the original DIC asymptotically.