A UNIFIED TREATMENT OF MULTIPLE TESTING WITH PRIOR KNOWLEDGE USING THE P-FILTER

• 成果类型: Article
• 署名作者: Ramdas, Aaditya K.; Barber, Rina F.; Wainwright, Martin J.; Jordan, Michael, I
• 署名单位: Carnegie Mellon University; University of Chicago; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1765
• 发表日期: 2019
• 页码: 2790-2821
• 关键词: false discovery rate

摘要

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.