Sample-Efficient Multiple Testing with Adaptive Data Collection

2026-09-22

AI Summary

本文研究了通过自适应数据收集解决多重测试问题，提出基于e值的后验抽样方法(e-PS)，有效控制错误发现率并减少样本需求。

Abstract

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.

Problem

• multiple testing
• adaptive data collection
• false discovery rate
• nonnull hypotheses

Innovation

• e-value-based posterior sampling
• adaptive experimental design
• false discovery rate control