The Annals of Statistics
- Ann. Statist.
- Volume 47, Number 5 (2019), 2790-2821.
A unified treatment of multiple testing with prior knowledge using the p-filter
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.
Ann. Statist., Volume 47, Number 5 (2019), 2790-2821.
Received: April 2017
Revised: September 2018
First available in Project Euclid: 3 August 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Ramdas, Aaditya K.; Barber, Rina F.; Wainwright, Martin J.; Jordan, Michael I. A unified treatment of multiple testing with prior knowledge using the p-filter. Ann. Statist. 47 (2019), no. 5, 2790--2821. doi:10.1214/18-AOS1765. https://projecteuclid.org/euclid.aos/1564797864
- Supplement to “A unified treatment of multiple testing with prior knowledge using the p-filter”. Contains details on dotfractions, generalized Simes tests for the global null and the LOOP property.