{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,26]],"date-time":"2026-10-26T17:29:17Z","timestamp":1793035757799,"version":"4.5.0"},"reference-count":42,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T00:00:00Z","timestamp":1775606400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["IIS-2229881"],"award-info":[{"award-number":["IIS-2229881"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["DMS-2310718"],"award-info":[{"award-number":["DMS-2310718"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In sequential anytime-valid inference, any admissible procedure must be based on e-processes: generalizations of test martingales that quantify the accumulated evidence against a composite null hypothesis at any stopping time. This paper proposes a method for combining e-processes constructed in different filtrations but for the same null. Although e-processes in the same filtration can be combined effortlessly (by averaging), e-processes in different filtrations cannot because their validity in a coarser filtration does not translate to a finer filtration. This issue arises in sequential tests of randomness and independence, as well as in the evaluation of sequential forecasters. We establish that a class of functions called adjusters can lift arbitrary e-processes across filtrations. The result yields a generally applicable \u2018adjust-then-combine\u2019 procedure, which we demonstrate on the problem of testing randomness in real-world financial data. Furthermore, we prove a characterization theorem for adjusters that formalizes a sense in which using adjusters is necessary. There are two major implications. First, if we have a powerful e-process in a coarsened filtration, then we readily have a powerful e-process in the original filtration. Second, when we coarsen the filtration to construct an e-process, there is a logarithmic cost to recovering validity in the original filtration.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkag058","type":"journal-article","created":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T12:24:51Z","timestamp":1773663891000},"page":"1492-1514","source":"Crossref","is-referenced-by-count":1,"title":["Combining evidence across filtrations"],"prefix":"10.1093","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0614-9477","authenticated-orcid":false,"given":"Yo Joong","family":"Choe","sequence":"first","affiliation":[{"name":"Decision Sciences Area, INSEAD Asia Campus , 1 Ayer Rajah Avenue, Singapore 138676 ,","place":["Singapore"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0497-311X","authenticated-orcid":false,"given":"Aaditya","family":"Ramdas","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, 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