Journal
ENTROPY
Volume 25, Issue 4, Pages -Publisher
MDPI
DOI: 10.3390/e25040618
Keywords
p-value calibration; Bayes factor; linear model; pseudo-p-value; adaptive levels
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This article proposes a method to adjust the minimum Bayes factor with information in order to approximate an exact Bayes factor, not only when p is a p-value but also when p is a pseudo-p-value. A version of the adjustment for linear models is also developed using the recent refinement of the Prior-Based BIC.
Minimum Bayes factors are commonly used to transform two-sided p-values to lower bounds on the posterior probability of the null hypothesis, in particular the bound -e . p . log(p). This bound is easy to compute and explain; however, it does not behave as a Bayes factor. For example, it does not change with the sample size. This is a very serious defect, particularly for moderate to large sample sizes, which is precisely the situation in which p-values are the most problematic. In this article, we propose adjusting this minimum Bayes factor with the information to approximate an exact Bayes factor, not only when p is a p-value but also when p is a pseudo -p-value. Additionally, we develop a version of the adjustment for linear models using the recent refinement of the Prior-Based BIC.
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