The Large Sample Correspondence between Classical Hypothesis Tests and Bayesian Posterior Odds Tests
证明，对于无趋势模型，点原假设与单侧或双侧备择假设的经典检验（Wald、LM、LR）与贝叶斯后验几率检验在大样本下等价，前提是备择假设下的先验以n^{-1/2}速率收缩到原假设。
This paper establishes a correspondence in large samples between classical hypothesis tests and Bayesian posterior odds tests for models without 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 priors, the Bayesian posterior odds test is equivalent in large samples to classical Wald, Lagrange multiplier, and likelihood ratio tests for some significance level and vice versa. The priors considered under the alternative hypothesis are taken to shrink to the null hypothesis at rate n[superscript -1/2] as the sample size n increases. Copyright 1994 by The Econometric Society.