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arXiv · 2609.26651

Sample-Efficient Multiple Testing with Adaptive Data Collection

Zhanran Lin·Wanteng Ma·Zhimei Ren·Yuting Wei
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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.

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Zhanran Lin, Wanteng Ma, Zhimei Ren, Yuting Wei. 2026-09-22. Sample-Efficient Multiple Testing with Adaptive Data Collection. https://arxiv.org/abs/2609.26651

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