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Activity Number: 450
Type: Contributed
Date/Time: Tuesday, August 11, 2015 : 3:05 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #317827
Title: The Validity of Bayesian Information Criteria in Misspecified Models
Author(s): Yoichi Miyata*
Companies: Takasaki City University of Economics
Keywords: Bayesian information criterion ; Laplace'method ; Model selection
Abstract:

Model selection has an important role in modern statistical analysis. Although BIC is derived by applying Laplace's method to the log-marginal likelihood functions, to show the validity of the approximations, we usually assume that a class of parametric models includes a correctly specified model. Lv and Liu (2014, Journal of the Royal Statistical Society Series B 76, 141-167) derive valid asymptotic expansions for the marginal likelihood functions in misspecified GLMs under some reasonable conditions, and propose the generalized BIC. In this talk, we derive a higher-order asymptotic expansion for the marginal likelihood functions under conditions similar to those of Lv and Liu, and present an alternative BIC criterion. However, we need a continuity condition on the prior density, which is stronger than that of Lv and Liu. We also present several numerical examples to illustrate the finite-sample performance of the alternative BIC in both correctly specified and misspecified logistic models.


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