Department of Statistics and Operations Research, University of Valencia, Valencia, Spain
Department of Statistical Science, Duke University, Durham, NC, USA
berger@stat.duke.edu,starf@ecnu.edu.cn
Department of Statistics, Seoul National University, Seoul, Korea
School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
Department of Mathematics, University of Puerto Rico, San Juan, Puerto Rico
Department of Psychology, University of Amsterdam, Amsterdam, Netherlands
ABSTRACT
We present a new approach to model selection and Bayes factor determination, based on Laplace expansions (as in BIC), which we call Prior-based Bayes Information Criterion (PBIC). In this approach, the Laplace expansion is only done with the likelihood function, and then a suitable prior distribution is chosen to allow exact computation of the (approximate) marginal likelihood arising from the Laplace approximation and the prior. The result is a closed-form expression similar to BIC, but now involves a term arising from the prior distribution (which BIC ignores) and also incorporates the idea that different parameters can have different effective sample sizes (whereas BIC only allows one overall sample size n). We also consider a modification of PBIC which is more favourable to complex models.