No. 912

Title:

Bayesian predictive information criterion for the evaluation of Bayesian models

Author(s):

Tomohiro, Ando (Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan.)

Key words:

Bayes model; Markov chain Monte Carlo; Model Misspecification; Model selection; Nonlinear regression.

Abstract:

    The problem of evaluating the goodness of the predictive distribution of the Bayes model is investigated from an information theoretic point of view. The Bayesian predictive information criterion is proposed as an estimator of the posterior mean of the expected log-likelihood of the predictive distribution when the specified family of probability distributions does not contain the true distribution. The proposed information criterion is developed by correcting the asymptotic bias of the posterior mean of the log-likelihood as an estimate of its expected log-likelihood. \par For illustration, the proposed information criterion is applied to the smoothing parameter selection problem in $P$-spline generalised linear models. We conduct Monte Carlo experiments to compare the performance of the proposed information criterion with other Bayesian model selection criteria, which include the deviance information criterion, Bayes factor and the cross validation predictive density approach. The simulation results show that the proposed information criterion performs very well in various situations.