Reconnecting p-value and Posterior Probability under One- and Two-sided Tests


Speaker:Guosheng Yin, University of Hong Kong
Host:Xiaolei Lin, School of Data Science, Fudan University
Time:10:00 - 11:00 am, Jan 13, 2020
Location:Zibin N102, Fudan University
Abstract:As a convention, p-value is often computed in frequentist hypothesis testing and compared with the nominal significance level of 0.05 to determine whether or not to reject the null hypothesis. The smaller the p-value, the more significant the statistical test. Under non-informative prior distributions, we establish the equivalence relationship between the p-value and Bayesian posterior probability of the null hypothesis for one-sided tests and, more importantly, the equivalence between the p-value and a transformation of posterior probabilities of the alternative hypotheses for two-sided tests. For two-sided hypothesis tests with a point null, we recast the problem as a combination of two one-sided hypotheses along the opposite directions and establish the notion of a “two-sided posterior probability”, which reconnects with the (two-sided) p-value. In contrast to common beliefs, such equivalence relationships render p-value an explicit interpretation of how strong the data support the null. Extensive simulation studies are conducted to demonstrate the equivalence relationship between the p-value and Bayesian posterior probability. Contrary to broad criticisms of the use of p-value in evidence-based studies, we justify its utility and reclaim its importance from the Bayesian perspective.

Prof. Guosheng Yin is the Patrick S C Poon Professor and head of the Department of Statistics and Actuarial Science at The University of Hong Kong. His research interests include statistical and intelligent learning for big data, Bayesian analysis, clinical trials, data mining and deep learning. He is currently the associate editor for JASA, Bayesian Analysis, Statistical Analysis and Data Mining, Contemporary Clinical trials, etc.