Open Access
November 2016 Consistency of Bayes factor for nonnested model selection when the model dimension grows
Min Wang, Yuzo Maruyama
Bernoulli 22(4): 2080-2100 (November 2016). DOI: 10.3150/15-BEJ720


Zellner’s $g$-prior is a popular prior choice for the model selection problems in the context of normal regression models. Wang and Sun [J. Statist. Plann. Inference 147 (2014) 95–105] recently adopt this prior and put a special hyper-prior for $g$, which results in a closed-form expression of Bayes factor for nested linear model comparisons. They have shown that under very general conditions, the Bayes factor is consistent when two competing models are of order $O(n^{\tau})$ for $\tau <1$ and for $\tau=1$ is almost consistent except a small inconsistency region around the null hypothesis. In this paper, we study Bayes factor consistency for nonnested linear models with a growing number of parameters. Some of the proposed results generalize the ones of the Bayes factor for the case of nested linear models. Specifically, we compare the asymptotic behaviors between the proposed Bayes factor and the intrinsic Bayes factor in the literature.


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Min Wang. Yuzo Maruyama. "Consistency of Bayes factor for nonnested model selection when the model dimension grows." Bernoulli 22 (4) 2080 - 2100, November 2016.


Received: 1 December 2014; Published: November 2016
First available in Project Euclid: 3 May 2016

zbMATH: 1358.62033
MathSciNet: MR3498023
Digital Object Identifier: 10.3150/15-BEJ720

Keywords: Bayes factor , growing number of parameters , model selection consistency , nonnested linear models , Zellner’s $g$-prior

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 4 • November 2016
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