Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

Collection Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2

Organizer(s) Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Date(s) 15/06/2020 - 19/06/2020
linked URL https://www.cirm-math.com/cirm-virtual-event-2146.html
00:00:00 / 00:00:00
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Post hoc bounds on false positives using reference families

By Pierre Neuvial

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.

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Citation data

  • DOI 10.24350/CIRM.V.19642003
  • Cite this video Neuvial, Pierre (08/06/2020). Post hoc bounds on false positives using reference families. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19642003
  • URL https://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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