Open Access
November 2012 Test procedures based on combination of Bayesian evidences for $H_{0}$
Rosangela H. Loschi, Cristiano C. Santos, Reinaldo B. Arellano-Valle
Braz. J. Probab. Stat. 26(4): 450-473 (November 2012). DOI: 10.1214/11-BJPS183


We introduce two procedures for testing which are based on pooling the posterior evidence for the null hypothesis provided by the full Bayesian significance test and the posterior probability for the null hypothesis. Although the proposed procedures can be used in more general situations, we focus attention in tests for a precise null hypothesis. We prove that the proposed procedure based on the linear operator is a Bayes rule. We also verify that it does not lead to the Jeffreys–Lindley paradox. For a precise null hypothesis, we prove that the procedure based on the logarithmic operator is a generalization of Jeffreys test. We apply the results to some well-known probability families. The empirical results show that the proposed procedures present good performances. As a by-product we obtain tests for normality under the skew-normal one.


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Rosangela H. Loschi. Cristiano C. Santos. Reinaldo B. Arellano-Valle. "Test procedures based on combination of Bayesian evidences for $H_{0}$." Braz. J. Probab. Stat. 26 (4) 450 - 473, November 2012.


Published: November 2012
First available in Project Euclid: 3 July 2012

zbMATH: 1319.62063
MathSciNet: MR2949088
Digital Object Identifier: 10.1214/11-BJPS183

Keywords: Asymmetric distributions , Bayes risk , Bayes tests , Jeffreys test , opinion pools

Rights: Copyright © 2012 Brazilian Statistical Association

Vol.26 • No. 4 • November 2012
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