A unified treatment of multiple testing with prior knowledge using the p-filter
This work addresses the challenge of improving statistical testing efficiency for researchers in fields like genomics or data science, though it appears incremental as it unifies existing methods rather than introducing a fundamentally new approach.
The authors tackled the problem of incorporating diverse forms of prior knowledge into multiple testing procedures to enhance power and precision, resulting in a unified algorithmic framework called p-filter that simultaneously handles four common types of prior knowledge and recovers various known algorithms as special cases.
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 non-uniform 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.