This paper explores a connection between empirical Bayes posterior distributions and false discovery rate (FDR) control. In the Gaussian sequence model, this work shows that empirical Bayes-calibrated spike and slab posterior distributions allow a correct FDR control under sparsity. Doing so, it offers a frequentist theoretical validation of empirical Bayes methods in the context of multiple testing. Our theoretical results are illustrated with numerical experiments.

中文翻译：

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关于尖峰和平板经验贝叶斯多重检验

本文探讨了经验贝叶斯后验分布与错误发现率 (FDR) 控制之间的联系。在高斯序列模型中，这项工作表明经验贝叶斯校准的尖峰和平板后验分布允许在稀疏情况下进行正确的 FDR 控制。这样做，它在多重测试的背景下提供了对经验贝叶斯方法的常客理论验证。我们的理论结果用数值实验来说明。