UNIFORMLY MOST POWERFUL BAYESIAN TESTS

doi:10.1214/13-AOS1123

2013-08-01

Johnson, Valen E. *

DOI：10.1214/13-AOS1123

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摘要

En 中文

Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the Bayesian setting by defining uniformly most powerful Bayesian tests to be tests that maximize the probability that the Bayes factor, in favor of the alternative hypothesis, exceeds a specified threshold. Like their classical counterpart, uniformly most powerful Bayesian tests are most easily defined in one-parameter exponential family models, although extensions outside of this class are possible. The connection between uniformly most powerful tests and uniformly most powerful Bayesian tests can be used to provide an approximate calibration between p-values and Bayes factors. Finally, issues regarding the strong dependence of resulting Bayes factors and p-values on sample size are discussed.

Keyword:

Bayes factor

Jeffreys-Lindley paradox

objective Bayes

one-parameter exponential family model

Neyman-Pearson lemma

nonlocal prior density

uniformly most powerful test

Higgs boson

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期刊

Annals of Statistics

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3.7

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2.8K

被引数:

2.9W

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