Title: The e-Partitioning Principle of False Discovery Rate Control Show Chinese title

Title: 错误发现率控制的e-划分原则

Abstract: We present a novel necessary and sufficient principle for False Discovery Rate (FDR) control. This e-Partitioning Principle says that a procedure controls FDR if and only if it is a special case of a general e-Partitioning procedure. By writing existing methods as special cases of this procedure, we can achieve uniform improvements of these methods, and we show this in particular for the eBH, BY and Su methods. We also show that methods developed using the $e$-Partitioning Principle have several valuable properties. They generally control FDR not just for one rejected set, but simultaneously over many, allowing post hoc flexibility for the researcher in the final choice of the rejected hypotheses. Under some conditions, they also allow for post hoc adjustment of the error rate, choosing the FDR level $\alpha$ post hoc, or switching to familywise error control after seeing the data. In addition, e-Partitioning allows FDR control methods to exploit logical relationships between hypotheses to gain power. Show Chinese abstract

Abstract: 我们提出了一种新的关于错误发现率（FDR）控制的必要且充分原则。 这一e-分割原则指出，一种过程只有在它是通用e-分割过程的一个特例时，才能控制FDR。 通过将现有方法写成该过程的特例，我们可以实现对这些方法的统一改进，并特别展示了对eBH、BY和Su方法的改进。 我们还表明，使用$e$-分割原则开发的方法具有多个有价值的特性。 它们通常不仅针对一个拒绝集控制FDR，而且可以同时在多个拒绝集中控制FDR，使研究人员在最终选择被拒绝的假设时具有事后灵活性。 在某些条件下，它们还允许事后调整误差率，事后选择FDR水平$\alpha$，或在查看数据后切换到族系误差控制。 此外，e-分割允许FDR控制方法利用假设之间的逻辑关系来提高功效。