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.
Publié le : 1994-12-14
Classification:
Likelihood principle,
conditional frequentist,
Bayes factor,
likelihood ratio,
significance,
Type I error,
Bayesian statistics,
stopping rule principle,
62A20,
62A15
@article{1176325757,
author = {Berger, James O. and Brown, Lawrence D. and Wolpert, Robert L.},
title = {A Unified Conditional Frequentist and Bayesian Test for Fixed and Sequential Simple Hypothesis Testing},
journal = {Ann. Statist.},
volume = {22},
number = {1},
year = {1994},
pages = { 1787-1807},
language = {en},
url = {http://dml.mathdoc.fr/item/1176325757}
}
Berger, James O.; Brown, Lawrence D.; Wolpert, Robert L. A Unified Conditional Frequentist and Bayesian Test for Fixed and Sequential Simple Hypothesis Testing. Ann. Statist., Tome 22 (1994) no. 1, pp. 1787-1807. http://gdmltest.u-ga.fr/item/1176325757/