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October 2019 A unified treatment of multiple testing with prior knowledge using the p-filter
Aaditya K. Ramdas, Rina F. Barber, Martin J. Wainwright, Michael I. Jordan
Ann. Statist. 47(5): 2790-2821 (October 2019). DOI: 10.1214/18-AOS1765


There is a significant literature on methods for incorporating knowledge into multiple testing procedures so as to improve their power and precision. Some common forms of prior knowledge include (a) beliefs about which hypotheses are null, modeled by nonuniform prior weights; (b) differing importances of hypotheses, modeled by differing penalties for false discoveries; (c) multiple arbitrary partitions of the hypotheses into (possibly overlapping) groups and (d) knowledge of independence, positive or arbitrary dependence between hypotheses or groups, suggesting the use of more aggressive or conservative procedures. We present a unified algorithmic framework called p-filter for global null testing and false discovery rate (FDR) control that allows the scientist to incorporate all four types of prior knowledge (a)–(d) simultaneously, recovering a variety of known algorithms as special cases.


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Aaditya K. Ramdas. Rina F. Barber. Martin J. Wainwright. Michael I. Jordan. "A unified treatment of multiple testing with prior knowledge using the p-filter." Ann. Statist. 47 (5) 2790 - 2821, October 2019.


Received: 1 April 2017; Revised: 1 September 2018; Published: October 2019
First available in Project Euclid: 3 August 2019

zbMATH: 07114929
MathSciNet: MR3988773
Digital Object Identifier: 10.1214/18-AOS1765

Primary: 60G10 , 62J15
Secondary: 62F03

Keywords: Adaptivity , Benjamini–Hochberg–Yekutieli , False discovery rate , group FDR , multiple testing , prior knowledge , Simes

Rights: Copyright © 2019 Institute of Mathematical Statistics


Vol.47 • No. 5 • October 2019
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