Hypothesis testing via posterior-test-based Bayes factors

• Main Authors: LI, Yong, WANG, Nianling, Jun YU, ZHANG, Yonghui
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2023
• Subjects: Bayes factor; Consistency; p-value; p-hacking; Posterior likelihood ratio test; Posterior Wald test; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2671; https://ink.library.smu.edu.sg/context/soe_research/article/3670/viewcontent/PLR36.pdf
• Institution: Singapore Management University

Hypothesis testing via p-value has been criticized in recent years. Bayes factors (BFs) have been tipped as a possible replacement of p-value for hypothesis testing. However, the standard BFs suffer from some theoretical and practical difficulties. For example, they are not well defined under improper priors and are subject to Jeffreys-Lindley-Bartlett’s paradox under vague priors. Moreover, they are difficult to compute for many models. In this paper, we propose to compare sampling distributions of the posterior-test-based statistics for hypothesis testing. Two posterior-test-based BFs are constructed from the posterior version of the likelihood ratio test and the Wald test, respectively. Under regularity conditions, we show that the new methods can avoid the p-hacking problem and the problems in the standard BFs. The advantages of the proposed methods are investigated using several simulation and empirical studies.