{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:58:13Z","timestamp":1787237893466,"version":"build-2736575974"},"reference-count":17,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T00:00:00Z","timestamp":1743033600000},"content-version":"vor","delay-in-days":85,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100010663","name":"European Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Union\u2019s Horizon 2020"},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01-ES028804"],"award-info":[{"award-number":["R01-ES028804"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01-ES035625"],"award-info":[{"award-number":["R01-ES035625"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-21-1-2510"],"award-info":[{"award-number":["N00014-21-1-2510"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,3,16]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Generalized linear models are routinely used for modelling relationships between a response variable and a set of covariates. The simple form of a generalized linear model comes with easy interpretability, but also leads to concerns about model misspecification impacting inferential conclusions. A popular semiparametric solution adopted in the frequentist literature is quasilikelihood, which improves robustness by only requiring correct specification of the first two moments. We develop a robust approach to Bayesian inference in generalized linear models through quasi-posterior distributions. We show that quasi-posteriors provide a coherent generalized Bayes inference method, while also approximating so-called coarsened posteriors. In so doing, we obtain new insights into the choice of coarsening parameter. Asymptotically, the quasi-posterior converges in total variation to a normal distribution and has important connections with the loss-likelihood bootstrap posterior. We demonstrate that it is also well calibrated in terms of frequentist coverage. Moreover, the loss-scale parameter has a clear interpretation as a dispersion, and this leads to a consolidated method-of-moments estimator.<\/jats:p>","DOI":"10.1093\/biomet\/asaf022","type":"journal-article","created":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T19:25:33Z","timestamp":1743362733000},"source":"Crossref","is-referenced-by-count":4,"title":["Bayesian inference for generalized linear models via quasi-posteriors"],"prefix":"10.1093","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-3067-0745","authenticated-orcid":false,"given":"D","family":"Agnoletto","sequence":"first","affiliation":[{"name":"Department of Statistical Science, Duke University , 214 Old Chemistry , Durham, North Carolina 27708,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9224-543X","authenticated-orcid":false,"given":"T","family":"Rigon","sequence":"additional","affiliation":[{"name":"Department of Economics, Management and Statistics, University of Milano\u2013Bicocca , Piazza dell'Ateneo Nuovo 1 , Milano 20126,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D B","family":"Dunson","sequence":"additional","affiliation":[{"name":"Department of Statistical Science, Duke University , 214 Old Chemistry , Durham, North Carolina 27708,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,3,27]]},"reference":[{"key":"2026032620013256400_asaf022-B1","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1111\/rssb.12158","article-title":"A general framework for updating belief distributions","volume":"78","author":"Bissiri","year":"2016","journal-title":"J. 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