A Short Note on Almost Sure Convergence of Bayes Factors in the General Set-Up

Article Type

Research Article

Publication Title

American Statistician

Abstract

Although there is a significant literature on the asymptotic theory of Bayes factor, the set-ups considered are usually specialized and often involves independent and identically distributed data. Even in such specialized cases, mostly weak consistency results are available. In this article, for the first time ever, we derive the almost sure convergence theory of Bayes factor in the general set-up that includes even dependent data and misspecified models. Somewhat surprisingly, the key to the proof of such a general theory is a simple application of a result of Shalizi to a well-known identity satisfied by the Bayes factor. Supplementary materials for this article are available online.

First Page

17

Last Page

20

DOI

10.1080/00031305.2017.1397548

Publication Date

1-2-2020

Comments

Open Access, Green

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