{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:25:37Z","timestamp":1787340337049,"version":"build-2736575974"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["818473"],"award-info":[{"award-number":["818473"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["318763901 - SFB1294"],"award-info":[{"award-number":["318763901 - SFB1294"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM\/ASA J. Uncertainty Quantification"],"published-print":{"date-parts":[[2024,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In statistical inference, a discrepancy between the parameter-to-observable map that generates the data and the parameter-to-observable map that is used for inference can lead to misspecified likelihoods and thus to incorrect estimates. In many inverse problems, the parameter-to-observable map is the composition of a linear state-to-observable map called an \u201cobservation operator\u201d and a possibly nonlinear parameter-to-state map called the \u201cmodel.\u201d We consider such Bayesian inverse problems where the discrepancy in the parameter-to-observable map is due to the use of an approximate model that differs from the best model, i.e., to nonzero \u201cmodel error.\u201d Multiple approaches have been proposed to address such discrepancies, each leading to a specific posterior. We show how to use local Lipschitz stability estimates of posteriors with respect to likelihood perturbations to bound the Kullback\u2013Leibler divergence of the posterior of each approach with respect to the posterior associated to the best model. Our bounds lead to criteria for choosing observation operators that mitigate the effect of model error for Bayesian inverse problems of this type. We illustrate the feasibility of one such criterion on an advection-diffusion-reaction PDE inverse problem and use this example to discuss the importance and challenges of model error-aware inference.<\/jats:p>","DOI":"10.1137\/23m1602140","type":"journal-article","created":{"date-parts":[[2024,7,10]],"date-time":"2024-07-10T04:01:24Z","timestamp":1720584084000},"page":"723-758","source":"Crossref","is-referenced-by-count":1,"title":["Choosing Observation Operators to Mitigate Model Error in Bayesian Inverse Problems"],"prefix":"10.1137","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7640-7347","authenticated-orcid":true,"given":"Nada","family":"Cvetkovi\u0107","sequence":"first","affiliation":[{"name":"Centre for Analysis, Scientific Computing and Applications, Eindhoven University of Technology, Eindhoven, the Netherlands."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6905-9903","authenticated-orcid":true,"given":"Han Cheng","family":"Lie","sequence":"additional","affiliation":[{"name":"Corresponding author. Institut f\u00fcr Mathematik, Universit\u00e4t Potsdam, Potsdam, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3606-499X","authenticated-orcid":true,"given":"Harshit","family":"Bansal","sequence":"additional","affiliation":[{"name":"Centre for Analysis, Scientific Computing and Applications, Eindhoven University of Technology, Eindhoven, the Netherlands."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3947-5882","authenticated-orcid":true,"given":"Karen","family":"Veroy","sequence":"additional","affiliation":[{"name":"Centre for Analysis, Scientific Computing and Applications, Eindhoven University of Technology, Eindhoven, the Netherlands."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,7,10]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-020-09926-w"},{"key":"ref2","unstructured":"A. Alexanderian, R. Nicholson, and N. Petra, Optimal Design of Large-scale Nonlinear Bayesian Inverse Problems Under Model Uncertainty, preprint, https:\/\/doi.org\/10.48550\/arXiv.2211.03952, 2022."},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/130933381"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/20M1347292"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/30\/11\/114007"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aaa34d"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2023.112104"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2005.04.004"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ad04ec"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199678792.001.0001"},{"key":"ref11","volume-title":"Partial Differential Equations","author":"Friedman A.","year":"2008"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1017\/9781139029834"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2020.2977067"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/17M1143344"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-09017-6"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/b138659"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.09.027"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00294"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1615\/Int.J.UncertaintyQuantification.v1.i1.10"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab89c5"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-23099-8_10"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/18M116544X"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aad91e"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1088\/0957-0233\/20\/10\/105504"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-49316-9"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1615\/Int.J.UncertaintyQuantification.2019027384"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1002\/kin.20906"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1093\/gji\/ggad116"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab6f43"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492910000061"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1145\/3428447"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1017\/9781108627771"}],"container-title":["SIAM\/ASA Journal on Uncertainty Quantification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/23M1602140","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:30:40Z","timestamp":1787337040000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M1602140"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,10]]},"references-count":32,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9,30]]}},"alternative-id":["10.1137\/23M1602140"],"URL":"https:\/\/doi.org\/10.1137\/23m1602140","relation":{},"ISSN":["2166-2525"],"issn-type":[{"value":"2166-2525","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,10]]}}}