Open Access
August 2013 Uniformly most powerful Bayesian tests
Valen E. Johnson
Ann. Statist. 41(4): 1716-1741 (August 2013). DOI: 10.1214/13-AOS1123


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.


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Valen E. Johnson. "Uniformly most powerful Bayesian tests." Ann. Statist. 41 (4) 1716 - 1741, August 2013.


Published: August 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1277.62084
MathSciNet: MR3127847
Digital Object Identifier: 10.1214/13-AOS1123

Primary: 62A01 , 62F03 , 62F05 , 62F15

Keywords: Bayes factor , Higgs boson , Jeffreys–Lindley paradox , Neyman–Pearson lemma , nonlocal prior density , objective Bayes , one-parameter exponential family model , uniformly most powerful test

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 4 • August 2013
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