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December 2014 Equivalence between the Posterior Distribution of the Likelihood Ratio and a p-value in an Invariant Frame
Isabelle Smith, André Ferrari
Bayesian Anal. 9(4): 939-962 (December 2014). DOI: 10.1214/14-BA877

Abstract

The Posterior distribution of the Likelihood Ratio (PLR) is proposed by Dempster in 1973 for significance testing in the simple vs. composite hypothesis case. In this hypothesis test case, classical frequentist and Bayesian hypothesis tests are irreconcilable, as emphasized by Lindley’s paradox, Berger & Selke in 1987 and many others. However, Dempster shows that the PLR (with inner threshold 1) is equal to the frequentist p-value in the simple Gaussian case. In 1997, Aitkin extends this result by adding a nuisance parameter and showing its asymptotic validity under more general distributions. Here we extend the reconciliation between the PLR and a frequentist p-value for a finite sample, through a framework analogous to the Stein’s theorem frame in which a credible (Bayesian) domain is equal to a confidence (frequentist) domain.

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Isabelle Smith. André Ferrari. "Equivalence between the Posterior Distribution of the Likelihood Ratio and a p-value in an Invariant Frame." Bayesian Anal. 9 (4) 939 - 962, December 2014. https://doi.org/10.1214/14-BA877

Information

Published: December 2014
First available in Project Euclid: 21 November 2014

zbMATH: 1327.62165
MathSciNet: MR3293963
Digital Object Identifier: 10.1214/14-BA877

Rights: Copyright © 2014 International Society for Bayesian Analysis

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Vol.9 • No. 4 • December 2014
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