Abstract：In large-scale hypothesis testing, computing exact $p$-values or $e$-values is often resource-intensive, creating a need for budget-aware inferential methods. We propose a general framework for active hypothesis testing that leverages inexpensive auxiliary statistics to allocate a global computational budget. For each hypothesis, our data-adaptive procedure probabilistically decides whether to compute the exact test statistic or a transformed proxy, guaranteeing a valid $p$-value or $e$-value while satisfying the exact budget constraint. Theoretical guarantees are established for our constructions, showing that the procedure achieves optimality for $e$-values and for $p$-values under independence, and admissibility for $p$-values under general dependence. Empirical results from simulations and two real-world applications, including a large-scale genome-wide association study (GWAS) and a clinical prediction task leveraging large language models (LLM), demonstrate that our framework improves statistical efficiency under fixed resource limits.

Bio：夏寅，复旦大学管理学院统计与数据科学系教授，博导，博士毕业于宾夕法尼亚大学，曾在美国北卡大学教堂山分校任tenure track助理教授。她2016年入选中组部千人计划青年项目；2020年获得国家自科基金优秀青年基金资助；2026年获国家自科基金青年科学基金A类资助。夏寅目前担任AOS、JASA和AOAS的编委，她的研究方向包括高维统计推断、联邦学习、大范围检验及应用等，她在JASA, AOS, JRSSB, Biometrika等期刊上发表三十余篇论文。