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© (2023), (Institute of Mathematical Statistics). All Rights Reserved.Modern data analysis frequently involves large-scale hypothesis testing, which naturally gives rise to the problem of maintaining control of a suitable type I error rate, such as the false discovery rate (FDR). In many biomedical and technological applications, an additional complexity is that hypotheses are tested in an online manner, one-by-one over time. However, traditional procedures that control the FDR, such as the Benjamini–Hochberg procedure, assume that all p-values are available to be tested at a single time point. To address these challenges, a new field of methodology has developed over the past 15 years showing how to control error rates for online multiple hypothesis testing. In this framework, hypotheses arrive in a stream, and at each time point the analyst decides whether to reject the current hypothesis based both on the evidence against it, and on the previous rejection decisions. In this paper, we present a comprehensive exposition of the literature on online error rate control, with a review of key theory as well as a focus on applied examples. We also provide simulation results comparing different online testing algorithms and an up-to-date overview of the many methodological extensions that have been proposed.
Author(s): Robertson DS, Wason JMS, Ramdas A
Publication type: Article
Publication status: Published
Journal: Statistical Science
Year: 2023
Volume: 38
Issue: 4
Pages: 557-575
Online publication date: 06/11/2023
Acceptance date: 02/04/2018
ISSN (print): 0883-4237
ISSN (electronic): 2168-8745
Publisher: Institute of Mathematical Statistics
URL: https://doi.org/10.1214/23-STS901
DOI: 10.1214/23-STS901
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