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.

中文翻译：

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经验贝叶斯方法用单独的先验来检验多个假设，用于左和右备选方案

我们在决策理论框架中考虑具有方向选择的多重假设问题。我们获得了一个受混合方向错误发现率约束的经验贝叶斯规则（mdFDR≤α) 在半参数设置下，检验统计量的分布是参数的，但先验分布是非参数的。我们为左尾和右尾替代方案提出了单独的先验，因为许多应用可能需要它。通过模拟将提议的贝叶斯规则与 Benjamini 和 Yekutieli 以及 Efron 提出的规则进行比较。我们为来自生物学实验的两组数据说明了建议的方法：HIV 转染的细胞系 mRNA 表达数据和数量性状全基因组 SNP 数据集。我们为建议的方法开发了一个用户友好的基于网络的闪亮应用程序，可通过 URL 获得https://npseb.shinyapps.io/npseb/. 可以直接访问 HIV 和 SNP 数据，并且可以执行本文提出的结果。