Bayesian Information Criteria

This chapter considers model selection and evaluation criteria from a Bayesian point of view. A general framework for constructing the Bayesian information criterion (BIC) is described. The BIC is also extended such that it can be applied to the evaluation of models estimated by regularization. Section 9.2 presents Akaike’s Bayesian information criterion (ABIC) developed for the evaluation of Bayesian models having prior distributions with hyperparameters. In the latter half of this chapter, we consider information criteria for the evaluation of predictive distributions of Bayesian models. In particular, Section 9.3 gives examples of analytical evaluations of bias correction for linear Gaussian Bayes models. Section 9.4 describes, for general Bayesian models, how to estimate the asymptotic biases and how to perform the second-order bias correction by means of Laplace’s method for integrals.