On the Null Distribution of Bayes Factors in Linear Regression
Abstract
© 2018 The Author(s). Published with license by Taylor & Francis We show that under
the null, the (Formula presented.) is asymptotically distributed as a weighted sum
of chi-squared random variables with a shifted mean. This claim holds for Bayesian
multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma
prior, the g-prior, and the normal prior. Our results have three immediate impacts.
First, we can compute analytically a p-value associated with a Bayes factor without
the need of permutation. We provide a software package that can evaluate the p-value
associated with Bayes factor efficiently and accurately. Second, the null distribution
is illuminating to some intrinsic properties of Bayes factor, namely, how Bayes factor
quantitatively depends on prior and the genesis of Bartlett’s paradox. Third, enlightened
by the null distribution of Bayes factor, we formulate a novel scaled Bayes factor
that depends less on the prior and is immune to Bartlett’s paradox. When two tests
have an identical p-value, the test with a larger power tends to have a larger scaled
Bayes factor, a desirable property that is missing for the (unscaled) Bayes factor.
Supplementary materials for this article are available online.
Type
Journal articlePermalink
https://hdl.handle.net/10161/17272Published Version (Please cite this version)
10.1080/01621459.2017.1328361Publication Info
Zhou, Quan; & Guan, Yongtao (2017). On the Null Distribution of Bayes Factors in Linear Regression. Journal of the American Statistical Association. pp. 1-10. 10.1080/01621459.2017.1328361. Retrieved from https://hdl.handle.net/10161/17272.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Yongtao Guan
Assistant Professor of Biostatistics & Bioinformatics

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