Prior-based Bayesian information criterion. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Bayarri, M. J.; Berger, James O.; Jang, Woncheol; Ray, Surajit; Pericchi, Luis R.; Visser, Ingmar
• Is Part Of: Statistical theory and related fields. Volume 3:Issue 1(2019)
• Page Start: 2
• Page End: 13
• Publication Date: 2019-01-02
• Subjects: Bayes factors -- model selection -- Cauchy priors -- consistency -- effective sample size -- Fisher information -- Laplace expansions -- robust priors; Statistics -- Periodicals; Statistics; Periodicals; Electronic journals; 001.422
• DOI: 10.1080/24754269.2019.1582126
• Languages: English
• ISSNs: 2475-4269

Abstract

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.