CIRM - Videos & books Library - Post hoc bounds on false positives using reference families

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Authors : Neuvial, Pierre (Author of the conference)
CIRM (Publisher )

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Abstract : We present confidence bounds on the false positives contained in subsets of selected null hypotheses. As the coverage probability holds simultaneously over all possible subsets, these bounds can be applied to an arbitrary number of possibly datadriven subsets.
These bounds are built via a two-step approach. First, build a family of candidate rejection subsets together with associated bounds, holding uniformly on the number of false positives they contain (call this a reference family). Then, interpolate from this reference family to find a bound valid for any subset.
This general program is exemplified for two particular types of reference families: (i) when the bounds are fixed and the subsets are p-value level sets (ii) when the subsets are fixed, spatially structured and the bounds are estimated.

Keywords : Multiple testing; selective inference

MSC Codes :
62J15 - Paired and multiple comparisons

Additional resources :
https://www.cirm-math.fr/RepOrga/2146/Slides/Neuvial_20200615_MMMS2.pdf

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Film maker :

Hennenfent, Guillaume

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https://videos.cirm-math.fr/2020-06-08_Neuvial.mp4

Information on the Event

Event Title : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2
Event 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.19642003
Cite this video as: Neuvial, Pierre (2020). Post hoc bounds on false positives using reference families. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19642003
URI : http://dx.doi.org/10.24350/CIRM.V.19642003

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Bibliography

BLANCHARD, Gilles, NEUVIAL, Pierre, et ROQUAIN, Etienne. On agnostic post hoc approaches to false positive control. arXiv preprint arXiv:1910.11575, 2019. - https://arxiv.org/abs/1910.11575

BLANCHARD, Gilles, NEUVIAL, Pierre, et ROQUAIN, Etienne. Post hoc confidence bounds on false positives using reference families. Annals of Statistics (to appear). - https://hal.archives-ouvertes.fr/hal-01483585v5

DURAND, Guillermo, BLANCHARD, Gilles, NEUVIAL, Pierre, et al. Post hoc false positive control for structured hypotheses. Scandinavian Journal of Statistics, 2020. - https://doi.org/10.1111/sjos.12453

GOEMAN, Jelle J., SOLARI, Aldo, et al. Multiple testing for exploratory research. Statistical Science, 2011, vol. 26, no 4, p. 584-597. - http://dx.doi.org/10.1214/11-STS356

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