title: Optimal multiple testing under a Gaussian prior on the effect sizes.
abstract: We develop a new method for large-scale frequentist multiple testing with Bayesian prior information. We find optimal [Formula: see text]-value weights that maximize the average power of the weighted Bonferroni method. Due to the nonconvexity of the optimization problem, previous methods that account for uncertain prior information are suitable for only a small number of tests. For a Gaussian prior on the effect sizes, we give an efficient algorithm that is guaranteed to find the optimal weights nearly exactly. Our method can discover new loci in genome-wide association studies and compares favourably to competitors. An open-source implementation is available.
authors.affiliation: Department of Statistics, Stanford University, Stanford, California 94305, U.S.A.
authors.forename: Edgar
authors.initials: E
authors.lastname: Dobriban
authors.affiliation: Department of Developmental Biology, Stanford University, Stanford, California 94305, U.S.A. kfortney@stanford.edu stuartkm@stanford.edu.
authors.forename: Kristen
authors.initials: K
authors.lastname: Fortney
authors.affiliation: Department of Developmental Biology, Stanford University, Stanford, California 94305, U.S.A. kfortney@stanford.edu stuartkm@stanford.edu.
authors.forename: Stuart K
authors.initials: SK
authors.lastname: Kim
authors.affiliation: Department of Statistics, Stanford University, Stanford, California 94305, U.S.A. owen@stanford.edu.
authors.forename: Art B
authors.initials: AB
authors.lastname: Owen
keywords: Genome-wide association study; Multiple testing; Nonconvex optimization; Weighted Bonferroni method; p-value weighting