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VOL. 57 | 2009 Bayesian Decision Theory for Multiple Comparisons


Applying a decision theoretic approach to multiple comparisons very similar to that described by Lehmann [Ann. Math. Statist. 21 (1950) 1–26; Ann. Math. Statist. 28 (1975a) 1–25; Ann. Math. Statist. 28 (1975b) 547–572], we introduce a loss function based on the concept of the false discovery rate (FDR). We derive a Bayes rule for this loss function and show that it is very closely related to a Bayesian version of the original multiple comparisons procedure proposed by Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289–300] to control the sampling theory FDR. We provide the results of a Monte Carlo simulation that illustrates the very similar sampling behavior of our Bayes rule and Benjamini and Hochberg’s procedure when applied to making all pair-wise comparisons in a one-way fixed effects analysis of variance setup with 10 and with 20 means.


Published: 1 January 2009
First available in Project Euclid: 3 August 2009

zbMATH: 1271.62020
MathSciNet: MR2681679

Digital Object Identifier: 10.1214/09-LNMS5719

Primary: 62C10 , 62F15 , 62J15

Keywords: Bayesian , decision theory , False discovery rate , loss function , Multiple comparisons

Rights: Copyright © 2009, Institute of Mathematical Statistics


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