Variable Selection for Bayesian Linear Regression Model in a Finite Sample Size

In Bayesian data analysis, a deviance information criterion (DIC)proposed by Spiegelhalter et al. (2002) is widely used for the modelselection, since this criterion is relatively easy to calculate and applicableto a wide range of statistical models. Spiegelhalter et al. (2002)gave an asymptotic justification of DIC in the case where the numberof observations grows with respect to the number of parameters.In small-sample cases, however, the estimated asymptotic bias of DICmight underestimate the true bias (Burnham, 2002). In this paper, wepropose a finite-sample bias corrected information criterion (ICBL) forthe Bayesian linear regression models with conjugate priors, as AICCproposed by Sugiura (1978) in frequentist framework. We examine theperformance of the proposed information criterion relative to the DICfor small-sample cases by simulation, and found that our proposedinformation criterion outperforms DIC