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

18 Mar 2017Aaditya RamdasRina Foygel BarberMartin J. WainwrightMichael I. Jordan

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... (read more)

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