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December 2003 The positive false discovery rate: a Bayesian interpretation and the q-value
John D. Storey
Ann. Statist. 31(6): 2013-2035 (December 2003). DOI: 10.1214/aos/1074290335


Multiple hypothesis testing is concerned with controlling the rate of false positives when testing several hypotheses simultaneously. One multiple hypothesis testing error measure is the false discovery rate (FDR), which is loosely defined to be the expected proportion of false positives among all significant hypotheses. The FDR is especially appropriate for exploratory analyses in which one is interested in finding several significant results among many tests. In this work, we introduce a modified version of the FDR called the "positive false discoveryrate" (pFDR). We discuss the advantages and disadvantages of the pFDR and investigate its statistical properties. When assuming the test statistics follow a mixture distribution, we show that the pFDR can be written as a Bayesian posterior probability and can be connected to classification theory. These properties remain asymptotically true under fairly general conditions, even under certain forms of dependence. Also, a new quantity called the "$q$-value" is introduced and investigated, which is a natural "Bayesian posterior p-value," or rather the pFDR analogue of the p-value.


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John D. Storey. "The positive false discovery rate: a Bayesian interpretation and the q-value." Ann. Statist. 31 (6) 2013 - 2035, December 2003.


Published: December 2003
First available in Project Euclid: 16 January 2004

MathSciNet: MR2036398
zbMATH: 1042.62026
Digital Object Identifier: 10.1214/aos/1074290335

Primary: 62F03

Keywords: $P$-values , $q$-values , Multiple comparisons , pFDR , pFNR , simultaneous inference

Rights: Copyright © 2003 Institute of Mathematical Statistics

Vol.31 • No. 6 • December 2003
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