THE LARGE-SAMPLE CORRESPONDENCE BETWEEN CLASSICAL HYPOTHESIS TESTS AND BAYESIAN POSTERIOR ODDS TESTS

This paper establishes a correspondence in large samples between class ical hypothesis tests and Bayesian posterior odds tests for models wit hout trends. More specifically, tests of point null hypotheses and one - or two-sided alternatives are considered (where nuisance parameters may be present under both hypotheses). It is shown that for certain pr iors the Bayesian posterior odds test is equivalent in large samples t o classical Wald, Lagrange multiplier, and likelihood ratio tests for some significance level and vice versa. The priors considered under th e alternative hypothesis are taken to shrink to the null hypothesis at rate n-1/2 as the sample size n increases.