{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T09:49:25Z","timestamp":1773395365280,"version":"3.50.1"},"reference-count":82,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["10.02 BAYES"],"award-info":[{"award-number":["10.02 BAYES"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2023,8]]},"DOI":"10.1137\/23m1556435","type":"journal-article","created":{"date-parts":[[2023,8,8]],"date-time":"2023-08-08T08:42:43Z","timestamp":1691484163000},"page":"831-865","source":"Crossref","is-referenced-by-count":24,"title":["Bayesian Inverse Problems Are Usually Well-Posed"],"prefix":"10.1137","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4600-0247","authenticated-orcid":true,"given":"Jonas","family":"Latz","sequence":"first","affiliation":[]}],"member":"351","published-online":{"date-parts":[[2023,8,8]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1515\/jip-2012-0071"},{"key":"atypb2","volume-title":"Probability & Measure Theory","author":"Ash R. B.","year":"2000","edition":"2"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-008-0196-6"},{"issue":"1763","key":"atypb4","first-page":"370","volume":"53","author":"Bayes T.","journal-title":"Philos. Trans. Roy. Soc. London"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-25040-3_23"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/17M1134214"},{"key":"atypb7","volume-title":"Probability and Measure","author":"Billingsley P.","year":"2008","edition":"3"},{"key":"atypb8","volume-title":"Pattern Recognition and Machine Learning","author":"Bishop C. M.","year":"2006"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/062"},{"key":"atypb10","first-page":"1237","volume":"8","author":"Bohra P.","year":"2022","journal-title":"IEEE Trans. Comput."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-01458-2"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/978-90-481-2785-6"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-0790-8_3"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/17M1139357"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1063\/1.4985359"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511813559"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1119\/1.1990764"},{"key":"atypb18","volume-title":"Nonparametric Bayesian Inference of Discretely Observed Diffusions, preprint, https:\/\/arxiv.org\/abs\/2004.04636","author":"Croix J. C.","year":"2000"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/29\/9\/095017"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/100814664"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-12385-1_7"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2018.09.019"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1214\/19-AOS1850"},{"key":"atypb24","volume-title":"Lipschitz Continuity of Probability Kernels in the Optimal Transport Framework, preprint, https:\/\/arxiv.org\/abs\/2010.08380","author":"Dolera E.","year":"2020"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2019.108627"},{"key":"atypb26","first-page":"1","volume":"19","author":"Dunlop M. M.","year":"2018","journal-title":"J. Mach. Learn. Res."},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-016-9704-8"},{"key":"atypb28","first-page":"2854","volume":"25","author":"Durmus A.","year":"2013","journal-title":"Bernoulli"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab1497"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1137\/140981319"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1081\/STM-200033117"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1111\/j.1751-5823.2002.tb00178.x"},{"key":"atypb33","volume-title":"Mathematical Foundations of Infinite-Dimensional Statistical Models","author":"Gin\u00e9 E.","year":"2016"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-0790-8_1"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1214\/20-ECP341"},{"key":"atypb36","first-page":"49","volume":"13","author":"Hadamard J.","year":"1902","journal-title":"Princeton Univ. Bull."},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/31\/8\/085009"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1909.136.210"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1137\/21M1406313"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1137\/16M1096372"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1137\/16M1076824"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/30\/11\/114001"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.4171\/IFB\/362"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511995569"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511790423"},{"key":"atypb46","volume-title":"Continuous-Time Stochastic Gradient Descent for Continuous Data, preprint, https:\/\/arxiv.org\/abs\/2112.03754","author":"Jin K.","year":"2021"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1137\/18M1210034"},{"key":"atypb48","first-page":"1","volume":"24","author":"Karvonen T.","year":"2023","journal-title":"J. Mach. Learn. Res."},{"key":"atypb49","volume-title":"Proceedings of the 3rd International Conference on Learning Representations (ICLR 2015)","author":"Kingma D. P.","year":"2015"},{"key":"atypb50","volume-title":"Proceedings of the International Conference on Learning Representations","author":"Kingma D. P.","year":"2014"},{"key":"atypb52","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ac7acd"},{"key":"atypb53","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/20\/5\/013"},{"key":"atypb54","doi-asserted-by":"publisher","DOI":"10.1137\/19M1247176"},{"key":"atypb55","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-021-10016-8"},{"key":"atypb56","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.02.003"},{"key":"atypb57","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.04.014"},{"key":"atypb58","doi-asserted-by":"publisher","DOI":"10.1137\/21M1406349"},{"key":"atypb59","first-page":"15","volume":"23","author":"Leao D.","year":"2004","journal-title":"Proyecciones"},{"key":"atypb60","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aadef2"},{"key":"atypb61","doi-asserted-by":"publisher","DOI":"10.1142\/S021820251650055X"},{"key":"atypb62","first-page":"1","volume":"18","author":"Mandt S.","year":"2017","journal-title":"J. Mach. Learn. Res."},{"key":"atypb63","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.2009.v6.p826"},{"key":"atypb64","first-page":"1225","volume":"30","author":"P","year":"2002","journal-title":"Ann. Statist."},{"key":"atypb65","volume-title":"Well-Posedness of Bayesian Inverse Problems for Hyperbolic Conservation Laws, preprint, https:\/\/arxiv.org\/abs\/2107.09701","author":"Mishra S.","year":"2021"},{"key":"atypb66","doi-asserted-by":"publisher","DOI":"10.1137\/1101016"},{"key":"atypb67","doi-asserted-by":"publisher","DOI":"10.1137\/0141016"},{"key":"atypb68","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729586"},{"key":"atypb69","doi-asserted-by":"publisher","DOI":"10.3150\/17-BEJ938"},{"key":"atypb70","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/28\/4\/045003"},{"key":"atypb71","doi-asserted-by":"publisher","DOI":"10.1007\/s10670-017-9936-9"},{"key":"atypb72","doi-asserted-by":"publisher","DOI":"10.1118\/1.1854779"},{"key":"atypb73","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab6f43"},{"key":"atypb74","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492910000061"},{"key":"atypb75","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3244"},{"key":"atypb76","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-23395-6"},{"key":"atypb77","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2017040"},{"key":"atypb78","doi-asserted-by":"publisher","DOI":"10.1002\/pamm.201710402"},{"key":"atypb79","first-page":"567","volume-title":"Proceedings of the 12th Conference on Artificial Intelligence and Statistics, PMLR","author":"Titsias M.","year":"2009"},{"key":"atypb80","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-71050-9"},{"key":"atypb81","volume-title":"Probability, Statistics, and Truth","author":"von Mises R.","year":"1939"},{"key":"atypb82","first-page":"681","volume-title":"Proceedings of the 28th International Conference on Machine Learning","author":"Welling M.","year":"2011"},{"key":"atypb83","doi-asserted-by":"publisher","DOI":"10.1080\/00036811.2022.2116014"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,8,16]],"date-time":"2023-08-16T12:41:13Z","timestamp":1692189673000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M1556435"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8]]},"references-count":82,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["10.1137\/23M1556435"],"URL":"https:\/\/doi.org\/10.1137\/23m1556435","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8]]}}}