A UNIFIED CONDITIONAL FREQUENTIST AND BAYESIAN TEST FOR FIXED AND SEQUENTIAL SIMPLE HYPOTHESIS-TESTING

被引:73
作者
BERGER, JO
BROWN, LD
WOLPERT, RL
机构
[1] UNIV PENN,DEPT STAT,PHILADELPHIA,PA 19104
[2] DUKE UNIV,INST STAT & DECIS SCI,DURHAM,NC 27708
关键词
LIKELIHOOD PRINCIPLE; CONDITIONAL FREQUENTIST; BAYES FACTOR; LIKELIHOOD RATIO; SIGNIFICANCE; TYPE I ERROR; BAYESIAN STATISTICS; STOPPING RULE PRINCIPLE;
D O I
10.1214/aos/1176325757
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
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.
引用
收藏
页码:1787 / 1807
页数:21
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