Hypothesis Testing Using Posterior-test-based Bayes Factor

Li Yong is a professor of economics at Renmin University of China. He obtained his Ph.D. degree in statistics from the Chinese University of Hongkong. He is currently the deputy dean of the School of Economics of Renmin University of China and concurrently the dean of the Department of Econometrics and Quantitative Economics. His main research interests are Bayesian financial econometrics, quantitative investment, and asset management. Professor Li has published nearly 50 academic articles in top Chinese and international Journals, including Journal of Econometrics (7 articles), Economic Research Journal, Management World. He also published and edit one academic monograph. He has won the second prize of Natural Science of the Ministry of Education and the third prize of Humanities and Social Sciences, and was selected into the New Century Talent Program of the Ministry of Education and the Beijing Excellent Young Talents Program.

Hypothesis testing based on p-values has been criticized in recent years. The conventional Bayes factors (BFs) have been tipped as possible replacements of p-values. However, conventional BFs suffer from several theoretical and practical difficulties. For example, the conventional BFs are not well-defined under improper priors and they subject to Jeffreys-Lindley-Bartlett's paradox when proper but vague priors are used. Moreover, they are difficult to compute for many models. In this paper, we propose to compare the sampling distributions of the posterior-test-based statistics for hypothesis testing. Two posterior-test-based statistics are considered, namely the posterior version of likelihood ratio (LR) test and the posterior version of Wald test. Under some regularity conditions, we establish the consistency property of the new method. We also show how the proposed method can address the problems in p-values and those in the conventional BFs. The advantages of the proposed method are highlighted using several simulation studies and empirical studies.