{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T12:36:09Z","timestamp":1792672569298,"version":"4.5.0"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T00:00:00Z","timestamp":1742947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000265","name":"UK Medical Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012338","name":"The Alan Turing Institute","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012338","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,9,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Standard Bayesian inference enables building models that combine information from various sources, but this inference may not be reliable if components of the model are misspecified. Cut inference, a particular type of modularized Bayesian inference, is an alternative that splits a model into modules and cuts the feedback from any suspect module. Previous studies have focused on a two module case, but a more general definition of a \u2018module\u2019 remains unclear. We present a formal definition of a \u2018module\u2019 and discuss its properties. We formulate methods for identifying modules; determining the order of modules; and building the cut distribution that should be used for cut inference within an arbitrary directed acyclic graph structure. We justify the cut distribution by showing that it not only cuts the feedback but also is the best approximation to the joint distribution satisfying this condition in Kullback\u2013Leibler divergence. We also extend cut inference for the two module case to a general multiple-module case via a sequential splitting technique and demonstrate this via illustrative applications.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkaf012","type":"journal-article","created":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T09:14:02Z","timestamp":1741857242000},"page":"1171-1199","source":"Crossref","is-referenced-by-count":4,"title":["A general framework for cutting feedback within modularized Bayesian inference"],"prefix":"10.1093","volume":"87","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7221-5877","authenticated-orcid":false,"given":"Yang","family":"Liu","sequence":"first","affiliation":[{"name":"MRC Biostatistics Unit, University of Cambridge , Cambridge, CB2 0SR ,","place":["UK"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9554-1499","authenticated-orcid":false,"given":"Robert J 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