## The Annals of Statistics

### The positive false discovery rate: a Bayesian interpretation and the q-value

John D. Storey

#### Abstract

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.

#### Article information

Source
Ann. Statist. Volume 31, Number 6 (2003), 2013-2035.

Dates
First available in Project Euclid: 16 January 2004

http://projecteuclid.org/euclid.aos/1074290335

Digital Object Identifier
doi:10.1214/aos/1074290335

Mathematical Reviews number (MathSciNet)
MR2036398

Zentralblatt MATH identifier
02067675

Subjects
Primary: 62F03: Hypothesis testing

#### Citation

Storey, John D. The positive false discovery rate: a Bayesian interpretation and the q -value. The Annals of Statistics 31 (2003), no. 6, 2013--2035. doi:10.1214/aos/1074290335. http://projecteuclid.org/euclid.aos/1074290335.

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