Variable Selection for Bayesian Linear Regression Model in a Finite Sample Size
Satoshi Kabe, Yuichiro Kanazawa · Institutional Repositories DataBase (IRDB) · 2013
In Bayesian data analysis a deviance information criterion (DIC) proposed by Spiegelhalter et al. (2002) is widely used for the model selection since this criterion is relatively easy to calculate and applicable to a wide range of statistical models. Spiegelhalter et al. (2002) gave an asymptotic justification of DIC in the case where the number of observations grows with respect to the number of parameters. In small-sample cases however the estimated asymptotic bias of DIC might underestimate the true bias (Burnham 2002). In this paper we propose a finite-sample bias corrected information criterion (ICBL) for the Bayesian linear regression models with conjugate priors as AICC proposed by Sugiura (1978) in frequentist framework. We examine the performance of the proposed information criterion relative to the DIC for small-sample cases by simulation and found that our proposed information criterion outperforms DIC.