Deviance information criterion (DIC) has beenextensively used for making Bayesian model selection. It is a Bayesian versionof AIC and chooses a model that gives the smallest expected Kullback-Leiblerdivergence between the data generating process (DGP) and a predictivedistribution asymptotically. We show that when the plug-in predictivedistribution is used, DIC can have a rigorous decision-theoretic justificationunder regularity conditions. An alternative expression for DIC, based on theBayesian predictive distribution, is proposed. The new DIC has a smallerpenalty term than the original DIC and is very easy to compute from the MCMCoutput. It is invariant to reparameterization and yields a smaller frequentistrisk than the original DIC asymptotically.
AIC, DIC, Bayesian Predictive Distribution, Plug-in Predictive Distribution, Loss Function, Bayesian Model Comparison, Frequentist Risk
Singapore Management University
City or Country
LI, Yong; Jun YU; and ZENG, Tao.
Deviance information criterion for Bayesian model selection: Justification and variation. (2017). 1-40. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1927
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