Normality of Posterior Distribution Under Misspecification and Nonsmoothness, and Bayes Factor for Davies' Problem
研究了在数据相依、模型误设且非光滑的广义框架下，贝叶斯过程的大样本性质，证明后验分布渐近正态，并分析了戴维斯检验问题中贝叶斯因子做出正确结论的概率趋近于1。
We examine the large sample properties of Bayes procedures in a general framework, where data may be dependent and models may be misspecified and nonsmooth. The posterior distribution of parameters is shown to be asymptotically normal, centered at the quasi maximum likelihood estimator, under mild conditions. In this framework, the Bayes factor for the test problem of Davies (1997, 1987 Davies , R. B. ( 1987 ). Hypothesis testing when a nuisance parameter is present only under the alternative . Biometrika 74 : 33 – 43 .[Web of Science ®] , [Google Scholar]), where a parameter is unidentified under the null hypothesis, is analyzed. The probability that the Bayes factor leads to a correct conclusion about the hypotheses in Davies’ problem is shown to approach to one.