{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/cost-aware-generalized-a-investing-for","title":"Cost-aware Generalized $α$-investing for Multiple Hypothesis Testing","arxiv_id":"2210.17514","date":"2022-10-31","proceeding":null,"authors":["Thomas Cook","Harsh Vardhan Dubey","Ji Ah Lee","Guangyu Zhu","Tingting Zhao","Patrick Flaherty"],"abstract":"We consider the problem of sequential multiple hypothesis testing with nontrivial data collection costs. This problem appears, for example, when conducting biological experiments to identify differentially expressed genes of a disease process. This work builds on the generalized $\\alpha$-investing framework which enables control of the false discovery rate in a sequential testing setting. We make a theoretical analysis of the long term asymptotic behavior of $\\alpha$-wealth which motivates a consideration of sample size in the $\\alpha$-investing decision rule. Posing the testing process as a game with nature, we construct a decision rule that optimizes the expected $\\alpha$-wealth reward (ERO) and provides an optimal sample size for each test. Empirical results show that a cost-aware ERO decision rule correctly rejects more false null hypotheses than other methods for $n=1$ where $n$ is the sample size. When the sample size is not fixed cost-aware ERO uses a prior on the null hypothesis to adaptively allocate of the sample budget to each test. We extend cost-aware ERO investing to finite-horizon testing which enables the decision rule to allocate samples in a non-myopic manner. Finally, empirical tests on real data sets from biological experiments show that cost-aware ERO balances the allocation of samples to an individual test against the allocation of samples across multiple tests.","url_abs":"https://arxiv.org/abs/2210.17514v3","url_pdf":"https://arxiv.org/pdf/2210.17514v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"cost-aware-generalized-a-investing-for","repo_url":"https://github.com/thomascook1437/cost-aware-alpha-investing","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}