A unified treatment of multiple testing with prior knowledge using the p-filter

By Aaditya Ramdas, Rina Foygel Barber, Martin J. Wainwright, Michael I. Jordan. Annals of Statistics, 2017

112 citations recorded by the source corpus.

A significant literature studies ways of employing prior knowledge to improve power and precision of multiple testing procedures. Some common forms of prior knowledge may include (a) \emph{a priori} beliefs about which hypotheses are null, modeled by non-uniform prior weights; (b) differing importances of hypotheses, modeled by differing penalties for false discoveries; (c) multiple arbitrary partitions of the hypotheses into known (possibly overlapping) groups, indicating (dis)similarity of hypotheses; and (d) knowledge of independence, positive dependence or arbitrary dependence between hypotheses or groups, allowing for more aggressive or conservative procedures. We unify a number of existing procedures, generalize the conditions under which they are known to work, and simplify their proofs of FDR control. Then, we present a unified algorithmic framework 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 wide variety of common algorithms as special cases.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/afc8c291aa589389e6c86407c16a5a646daddaaf

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In Management Science and Operations Research

1. Aaditya Ramdas
2. Ruodu Wang
3. Robert Tibshirani
4. E.J. Candes
5. Rina Foygel Barber
6. Matthew F. Dixon

In Statistics and Probability

1. E.J. Candes
2. Aaditya Ramdas
3. Rina Foygel Barber
4. Robert Tibshirani
5. Ruodu Wang
6. Martin J. Wainwright
7. Peter Buhlmann
8. Stefan Wager

Citations in the corpus

• Conformal prediction beyond exchangeability (2022, methodology): “The case where p1 = · · · = pn (and a1, . . . , an are arbitrary) can be found in [Ramdas et al., 2019, Lemma 3] and is used for proving FDR control for a hierarchical multiple testing procedure (the p-filter).”
• False discovery rate control with e‐values (2020, methodology): “We anticipate this lemma to aid with the design and proof of FDR procedures with e-values in other contexts—just as the corresponding p-value lemma already has Ramdas et al. (2019b)—and we shall see how it is applied to e-BH next.”