Article ID: | iaor2017841 |
Volume: | 59 |
Issue: | 1 |
Start Page Number: | 43 |
End Page Number: | 56 |
Publication Date: | Mar 2017 |
Journal: | Australian & New Zealand Journal of Statistics |
Authors: | Zhang Jin |
Keywords: | experiment, statistics: experiment, testing |
A fundamental theorem in hypothesis testing is the Neyman‐Pearson (N‐P) lemma, which creates the most powerful test of simple hypotheses. In this article, we establish Bayesian framework of hypothesis testing, and extend the Neyman‐Pearson lemma to create the Bayesian most powerful test of general hypotheses, thus providing optimality theory to determine thresholds of Bayes factors. Unlike conventional Bayes tests, the proposed Bayesian test is able to control the type I error.