ArticleJournal of the American Statistical Association2018
On the Null Distribution of Bayes Factors in Linear Regression.
Article in Journal of the American Statistical Association, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- Reflection knockoffs via householder reflection: applications in proteomics and genetic fine mapping.Genetics · 2025Article
- Abundant Parent-of-origin Effect eQTL: The Framingham Heart Study.bioRxiv : the preprint server for biology · 2025Article
- The Bayesian lens and Bayesian blinkers.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2023Review
- Wavelet Screening identifies regions highly enriched for differentially methylated loci for orofacial clefts.NAR genomics and bioinformatics · 2021Article
- A fast wavelet-based functional association analysis replicates several susceptibility loci for birth weight in a Norwegian population.BMC genomics · 2021Article
- BayesSMILES: Bayesian Segmentation Modeling for Longitudinal Epidemiological Studies.medRxiv : the preprint server for health sciences · 2021Article
- Fast Bayesian inference in large Gaussian graphical models.Biometrics · 2019Article
- Fast Model-Fitting of Bayesian Variable Selection Regression Using the Iterative Complex Factorization Algorithm.Bayesian analysis · 2019Article
- Functional annotation and Bayesian fine-mapping reveals candidate genes for important agronomic traits in Holstein bulls.Communications biology · 2019Article
- Multiscale parcellation of dynamic causal models of the brain.Imaging neuroscience (Cambridge, Mass.)Article
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2 authors.
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Abstract
We show that under the null, the 2 log(Bayes factor) 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.
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