On the Null Distribution of Bayes Factors in Linear Regression

Thumbnail Image



Journal Title

Journal ISSN

Volume Title

Repository Usage Stats


Citation Stats


© 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.






Published Version (Please cite this version)


Publication Info

Zhou, Quan, and Yongtao Guan (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.

Unless otherwise indicated, scholarly articles published by Duke faculty members are made available here with a CC-BY-NC (Creative Commons Attribution Non-Commercial) license, as enabled by the Duke Open Access Policy. If you wish to use the materials in ways not already permitted under CC-BY-NC, please consult the copyright owner. Other materials are made available here through the author’s grant of a non-exclusive license to make their work openly accessible.