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Online Multiple Hypothesis Testing

Lookup NU author(s): Professor James WasonORCiD

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Abstract

© (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.


Publication metadata

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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