The highly influential two‐group model in testing a large number of statistical hypotheses assumes that the test statistics are drawn independently from a mixture of a high probability null distribution and a low probability alternative. Optimal control of the marginal false discovery rate (mFDR), in the sense that it provides maximal power (expected true discoveries) subject to mFDR control, is known to be achieved by thresholding the local false discovery rate (locFDR), the probability of the hypothesis being null given the set of test statistics, with a fixed threshold. We address the challenge of controlling optimally the popular false discovery rate (FDR) or positive FDR (pFDR) in the general two‐group model, which also allows for dependence between the test statistics. These criteria are less conservative than the mFDR criterion, so they make more rejections in expectation. We derive their optimal multiple testing (OMT) policies, which turn out to be thresholding the locFDR with a threshold that is a function of the entire set of statistics. We develop an efficient algorithm for finding these policies, and use it for problems with thousands of hypotheses. We illustrate these procedures on gene expression studies.

中文翻译：

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两组模型中错误发现准则的最优控制

在测试大量统计假设时极具影响力的两组模型假定，检验统计数据是独立于高概率零分布和低概率替代方法的混合得出的。已知通过对局部错误发现率（locFDR）进行阈值化，可以实现对边缘错误发现率（mFDR）的最佳控制，因为它可以提供受mFDR控制的最大功率（预期的真实发现）。对于给定的检验统计量，具有固定阈值的假设为空。我们解决了在一般的两组模型中最佳控制流行的误发现率（FDR）或正FDR（pFDR）的挑战，这也使得测试统计数据之间具有依赖性。这些标准不如mFDR标准保守，因此他们对期望的拒绝更多。我们推导了他们的最佳多重测试（OMT）策略，结果证明该locFDR的阈值是整个统计数据集的函数。我们开发了一种有效的算法来查找这些策略，并将其用于成千上万个假设的问题。我们在基因表达研究中说明了这些程序。