A UNIFIED CONDITIONAL FREQUENTIST AND BAYESIAN TEST FOR FIXED AND SEQUENTIAL SIMPLE HYPOTHESIS-TESTING
成果类型：
Article
署名作者：
BERGER, JO; BROWN, LD; WOLPERT, RL
署名单位：
University of Pennsylvania; Duke University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176325757
发表日期：
1994
页码：
1787-1807
关键词：
摘要：
Preexperimental frequentist error probabilities are arguably inadequate, as summaries of evidence from data, in many hypothesis-testing settings. The conditional frequentist may respond to this by identifying certain subsets of the outcome space and reporting a conditional error probability, given the subset of the outcome space in which the observed data lie. Statistical methods consistent with the likelihood principle, including Bayesian methods, avoid the problem by a more extreme form of conditioning. In this paper we prove that the conditional frequentist's method can be made exactly equivalent to the Bayesian's in simple versus simple hypothesis testing: specifically, we find a conditioning strategy for which the conditional frequentist's reported conditional error probabilities are the same as the Bayesian's posterior probabilities of error. A conditional frequentist who uses such a strategy can exploit other features of the Bayesian approach-for example, the validity of sequential hypothesis tests (including versions of the sequential probability ratio test, or SPRT) even if the stopping rule is incompletely specified.