Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Lin, Zhanran, Ma, Wanteng, Ren, Zhimei, Wei, Yuting
Institution: University of Pennsylvania
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Awards: CAREER: Statistical Learning from a Modern Perspective: Over-parameterization, Regularization, and Generalization, CIF: Small: Non-Asymptotic Foundations of Approximate Message Passing, Collaborative Research: CIF: Medium: Statistical and Algorithmic Foundations of Efficient Reinforcement Learning, Trusted selective and predictive inference tools for modern data-driven applications
OpenAlex ID: W7214128849