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

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1303 Scopus citations


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 discovery rate" (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.

Original languageAmerican English
Pages (from-to)2013-2035
Number of pages23
JournalAnnals of Statistics
Issue number6
StatePublished - Dec 2003
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Multiple comparisons
  • Simultaneous inference
  • p-values
  • pFDR
  • pFNR
  • q-values


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