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Optimal control of false discovery criteria in the general two-group model
Virtualconference
Authors : Heller, Ruth (Author of the conference)
CIRM (Publisher )
62F03 - Hypothesis testing
62J15 - Paired and multiple comparisons
62P10 - Applications of statistics to biology and medical sciences
Additional resources :
https://www.cirm-math.fr/RepOrga/2146/Slides/RuthHeller.pdf
CIRM (Publisher )
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Abstract :
The highly influential two-group model in testing a large number of statistical hypotheses assumes that the test statistics are drawn independently from a mixture of a high probability null distribution and a low probability alternative. Optimal control of the marginal false discovery rate (mFDR), in the sense that it provides maximal power (expected true discoveries) subject to mFDR control, is known to be achieved by thresholding the local false discovery rate (locFDR), i.e., the probability of the hypothesis being null given the set of test statistics, with a fixed threshold.
We address the challenge of controlling optimally the popular false discovery rate (FDR) or positive FDR (pFDR) rather than mFDR in the general two-group model, which also allows for dependence between the test statistics. These criteria are less conservative than the mFDR criterion, so they make more rejections in expectation.
We derive their optimal multiple testing (OMT) policies, which turn out to be thresholding the locFDR with a threshold that is a function of the entire set of statistics. We develop an efficient algorithm for finding these policies, and use it for problems with thousands of hypotheses. We illustrate these procedures on gene expression studies.
Keywords : Multiple testing; false discovery rate; positive FDR; infinite linear programming; large scale inference
MSC Codes : We address the challenge of controlling optimally the popular false discovery rate (FDR) or positive FDR (pFDR) rather than mFDR in the general two-group model, which also allows for dependence between the test statistics. These criteria are less conservative than the mFDR criterion, so they make more rejections in expectation.
We derive their optimal multiple testing (OMT) policies, which turn out to be thresholding the locFDR with a threshold that is a function of the entire set of statistics. We develop an efficient algorithm for finding these policies, and use it for problems with thousands of hypotheses. We illustrate these procedures on gene expression studies.
Keywords : Multiple testing; false discovery rate; positive FDR; infinite linear programming; large scale inference
62F03 - Hypothesis testing
62J15 - Paired and multiple comparisons
62P10 - Applications of statistics to biology and medical sciences
Additional resources :
https://www.cirm-math.fr/RepOrga/2146/Slides/RuthHeller.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/06/2020 Conference Date : 03/06/2020 Subseries : Research talks arXiv category : Statistics Theory ; Methodology Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:38:07 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2020-06-03_Heller.mp4 
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Information on the Event
Event Title : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2Event Organizers : Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne Dates : 15/06/2020 - 19/06/2020 Event Year : 2020 Event URL : https://www.cirm-math.com/cirm-virtual-...
Citation Data
DOI : 10.24350/CIRM.V.19640903Cite this video as: Heller, Ruth (2020). Optimal control of false discovery criteria in the general two-group model. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19640903 URI : http://dx.doi.org/10.24350/CIRM.V.19640903 |
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Bibliography
- ROSSET, Saharon. Optimal control of false discovery criteria in the two-group model. arXiv preprint arXiv:1902.00892, 2019. - https://arxiv.org/abs/1902.00892
