Brazilian Journal of Probability and Statistics

Bayesian hypothesis testing: Redux

Hedibert F. Lopes and Nicholas G. Polson

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Abstract

Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter values, we revisit the seminal paper of Edwards, Lindman and Savage (Psychol. Rev. 70 (1963) 193–242). There are a number of important take-aways from comparing the Bayesian paradigm via Bayes factors to frequentist ones. We provide examples where evidence for a Bayesian strikingly supports the null, but leads to rejection under a classical test. Finally, we conclude with directions for future research.

Article information

Source
Braz. J. Probab. Stat., Volume 33, Number 4 (2019), 745-755.

Dates
Received: August 2018
Accepted: April 2019
First available in Project Euclid: 26 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1566806431

Digital Object Identifier
doi:10.1214/19-BJPS442

Mathematical Reviews number (MathSciNet)
MR3996315

Keywords
Bayesian hypothesis testing Bayes factor $p$-value test statistic multiple comparisons

Citation

Lopes, Hedibert F.; Polson, Nicholas G. Bayesian hypothesis testing: Redux. Braz. J. Probab. Stat. 33 (2019), no. 4, 745--755. doi:10.1214/19-BJPS442. https://projecteuclid.org/euclid.bjps/1566806431


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