Laplace approximations and Bayesian information criteria in possibly misspecified models

Yoichi Miyata

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 24, 12240-12258

Abstract: We provide general conditions to ensure the valid Laplace approximations to the marginal likelihoods under model misspecification, and derive the Bayesian information criteria including all terms of order Op(1). Under conditions in theorem 1 of Lv and Liu [J. R. Statist. Soc. B, 76, (2014), 141–167] and a continuity condition for prior densities, asymptotic expansions with error terms of order op(1) are derived for the log-marginal likelihoods of possibly misspecified generalized linear models. We present some numerical examples to illustrate the finite sample performance of the proposed information criteria in misspecified models.

Date: 2017
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DOI: 10.1080/03610926.2017.1295079

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