False Discovery Rate (FDR)

A False Discovery Rate (FDR) is a Predictive Relation Performance Metric based on the Proportion of False Positive Predictions to True Cases.

• Context:
  • It can be estimated by: FP / (TP + FN).
  • It can be used in multi random experiments to identify the proportion of false discoveries over true discoveries.
  • …
• See: False Positive Rate, Significance Level.

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References

2020

• (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/false_discovery_rate Retrieved:2020-3-25.
  • The false discovery rate (FDR) is a method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons. FDR-controlling procedures are designed to control the expected proportion of "discoveries" (rejected null hypotheses) that are false (incorrect rejections). FDR-controlling procedures provide less stringent control of Type I errors compared to familywise error rate (FWER) controlling procedures (such as the Bonferroni correction), which control the probability of at least one Type I error. Thus, FDR-controlling procedures have greater power, at the cost of increased numbers of Type I errors.

2004

• http://www.nature.com/nrg/journal/v4/n9/glossary/nrg1155_glossary.html
  • FALSE DISCOVERY RATE (FDR). The proportion of false-positive test results out of all positive (significant) tests (note that the FDR is conceptually different to the significance level).
  • SIGNIFICANCE LEVEL The proportion of false-positive test results out of all false results — that is, results that are obtained when the effect investigated is known to be absent (see also false discovery rate).

2003

• John D. Storey. (2003). “The Positive False Discovery Rate: A Bayesian Interpretation and the q-Value." Institute of Mathematical Statistics.
  • 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 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.

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