Deviance information criterion for Bayesian model selection: Justification and variation

• Main Authors: LI, Yong, Jun YU, ZENG, Tao
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2017
• Subjects: AIC; DIC; Bayesian Predictive Distribution; Plug-in Predictive Distribution; Loss Function; Bayesian Model Comparison; Frequentist Risk; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1927; https://ink.library.smu.edu.sg/context/soe_research/article/2926/viewcontent/DICTheory10.pdf
• Institution: Singapore Management University

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.