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From p-Values to Posterior Probabilities of Null Hypotheses
Daiver Vélez Ramos1, Luis R Pericchi Guerra2, María Eglée Pérez Hernández2
1Faculty of Business Administration, Statistical Institute and Computerized Information Systems, Río Piedras Campus, University of Puerto Rico, 15 AVE Universidad STE 1501, San Juan, PR 00925-2535, USA.
Abstract:
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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