LAUSR

We consider a multiple hypotheses testing problem with directional alternatives in a decision theoretic framework. Considering non-symmetric alternative hypotheses, we show that the skewness in the alternatives permits the Bayes rule to make more correct discoveries than if the alternatives are symmetric. We obtain a Bayes rule under a Lebesgue prior (non-informative) subject to a constraint on mixed directional false discovery rate $${\varvec{mdFDR}} \le {\varvec{\alpha}}$$ . The proposed Bayes rule is compared through simulation against rules proposed by Benjamini and Yekutieli (J Am Stat Assoc 100(469):71–80, 2005) and Efron (Ann Stat 35(4):1531–1377, 2007; J Am Stat Assoc 102(477):93–103, 2007). 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.