UNIFORMLY MOST POWERFUL BAYESIAN TESTS. Academic Article

abstract

• 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.

authors

• Johnson, Valen

published proceedings

• Ann Stat

altmetric score

• 7.58

author list (cited authors)

• Johnson, V. E.

citation count

• 65

complete list of authors

• Johnson, Valen E

publication date

• August 2013

publisher

• Institute of Mathematical Statistics  Publisher

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

PubMed Central ID

• 24659829

Digital Object Identifier (DOI)

• 10.1214/13-AOS1123

URI

• https://hdl.handle.net/1969.1/179872

start page

• 1716

end page

• 1741

volume

• 41

issue

• 4

URL

• http%3A%2F%2Fdx.doi.org%2F10.1214%2F13-aos1123