# Sample-Efficient Multiple Testing with Adaptive Data Collection

arXiv: https://arxiv.org/abs/2609.26651 · HTML: https://mlsanity.com/paper/2609.26651/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2026.

## Built on by (most cited first, 1 of 1)

- [Always-On Experimentation](https://mlsanity.com/paper/2609.38695/) (2026)

## Abstract (arXiv)

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.