Empirical Bayesian approach to testing multiple hypotheses with separate priors for left and right alternatives

Bansal Naveen K., Maadooliat Mehdi () and Schrodi Steven J.
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Bansal Naveen K.: Department of Mathematics, Statistics, and Computer Sciences, Marquette University, Milwaukee, WI 53201-1881, USA
Maadooliat Mehdi: Department of Mathematics, Statistics, and Computer Sciences, Marquette University, Milwaukee, WI 53201-1881, USA
Schrodi Steven J.: Center for Human Genetics, Marshfield Clinic Research Institute, Marshfield, WI 54449, USA

Statistical Applications in Genetics and Molecular Biology, 2018, vol. 17, issue 4, 13

Abstract: We consider a multiple hypotheses problem with directional alternatives in a decision theoretic framework. We obtain an empirical Bayes rule subject to a constraint on mixed directional false discovery rate (mdFDR≤α) under the semiparametric setting where the distribution of the test statistic is parametric, but the prior distribution is nonparametric. We proposed separate priors for the left tail and right tail alternatives as it may be required for many applications. The proposed Bayes rule is compared through simulation against rules proposed by Benjamini and Yekutieli and Efron. We illustrate the proposed methodology for two sets of data from biological experiments: HIV-transfected cell-line mRNA expression data, and a quantitative trait genome-wide SNP data set. We have developed a user-friendly web-based shiny App for the proposed method which is available through URL https://npseb.shinyapps.io/npseb/. The HIV and SNP data can be directly accessed, and the results presented in this paper can be executed.

Keywords: directional alternatives; EM algorithm; false discovery rates; HIV; SNP (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1515/sagmb-2018-0002

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