发表机构
University of Pennsylvania（宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于e值的后验采样程序，在自适应多重检验中控制错误发现率并保证嵌套拒绝集，通过理论界和实验验证其样本高效性。
AI 中文摘要
本文研究了多重检验中的自适应实验设计问题，其中实验者顺序选择要采样的假设。我们提出了基于e值的后验采样（e-PS）程序，该程序利用对数e值增量的经验平均值来指导随机采样，并应用e-BH构建拒绝集。在条件有效的e值增量下，该程序在任意停止时间控制错误发现率，并产生嵌套拒绝集。我们建立了发现所有非零假设所需样本数的高概率界，这些界以底层e过程的增长和集中性表示。我们将这些界专门应用于简单对简单、复合对简单以及简单对复合检验。使用笑话评分和水印文本的模拟与实验展示了该程序在有限采样预算下的功效。
英文摘要
This paper studies adaptive experimental design for multiple testing, where an experimenter sequentially chooses which hypothesis to sample. We propose the e-value-based posterior sampling (e-PS) procedure, which uses the empirical average of log e-value increments to guide randomized sampling and applies e-BH to construct rejection sets. Under conditionally valid e-value increments, the procedure controls the false discovery rate at arbitrary stopping times and produces nested rejection sets. We establish high-probability bounds on the number of samples needed to discover all nonnull hypotheses in terms of the growth and concentration of the underlying e-processes. We specialize these bounds to simple-versus-simple, composite-versus-simple, and simple-versus-composite testing. Simulations and experiments using joke ratings and watermarked text illustrate the procedure's power under limited sampling budgets.
