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December, 1994 A Unified Conditional Frequentist and Bayesian Test for Fixed and Sequential Simple Hypothesis Testing
James O. Berger, Lawrence D. Brown, Robert L. Wolpert
Ann. Statist. 22(4): 1787-1807 (December, 1994). DOI: 10.1214/aos/1176325757


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.


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James O. Berger. Lawrence D. Brown. Robert L. Wolpert. "A Unified Conditional Frequentist and Bayesian Test for Fixed and Sequential Simple Hypothesis Testing." Ann. Statist. 22 (4) 1787 - 1807, December, 1994.


Published: December, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0824.62002
MathSciNet: MR1329168
Digital Object Identifier: 10.1214/aos/1176325757

Primary: 62A20
Secondary: 62A15

Keywords: Bayes factor , Bayesian statistics , conditional frequentist , likelihood principle , likelihood ratio , significance , stopping rule principle , Type I error

Rights: Copyright © 1994 Institute of Mathematical Statistics

Vol.22 • No. 4 • December, 1994
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