Asymptotic normality with small relative errors of posterior probabilities of half-spaces

• 成果类型: Article
• 署名作者: Dudley, RM; Haughton, D
• 署名单位: Massachusetts Institute of Technology (MIT); Bentley University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2002
• 页码: 1311-1344
• 关键词: tail probabilities; Bayes Factors; approximations; expansions; likelihood; MODEL; distributions; INTEGRALS; BEHAVIOR; moments

摘要

Let Theta be a parameter space included in a finite-dimensional Euclidean space and let A be a half-space. Suppose that the maximum likelihood estimate theta(n) of theta is not in A (otherwise, replace A by its complement) and let A be the maximum log likelihood (at theta(n)) minus the maximum log likelihood over the boundary partial derivativeA. It is shown that under some conditions, uniformly over all half-spaces A, either the posterior probability of A is asymptotic to Phi (-root2Delta) where Phi is the standard normal distribution function, or both the posterior probability and its approximant go to 0 exponentially in n. Sharper approximations depending. on the prior are also defined.