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Title: All-resolution inference: Consistent confidence bounds for the false discovery proportion in high-dimensional data Authors:  Jelle Goeman - Leiden University Medical Center (Netherlands) [presenting]
Aldo Solari - University of Milano-Bicocca (Italy)
Abstract: The combination of closed testing with the Simes inequality can be used to derive simultaneous upper confidence bounds for the false discovery proportion (FDP) in all subsets of the hypotheses. Consequently, these bounds are valid even when these subsets are chosen post hoc. This property is useful e.g. in neuroscience, where it can be used to find interesting brain regions and to infer the percentage of activation in those brain regions, all in the same data, or in gene expression data, where it may be used to do gene set testing without requiring that the database of gene sets is chosen before seeing the data. We investigate the power properties of this method in large problems, showing that the procedure is remarkably powerful given the enormous simultaneity. We show that (1.) if sufficient signal is present, as the number of hypothesis goes to infinity, the number of discoveries allowed at any FDP-level also goes to infinity. We also show that (2.) the lower bound of the FDP seen as an estimator of FDP is uniformly consistent with respect to the size of the multiple testing problem.