{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T03:17:58Z","timestamp":1787455078688,"version":"build-2736575974"},"reference-count":78,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2237628"],"award-info":[{"award-number":["DMS-2237628"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0022232"],"award-info":[{"award-number":["DE-SC0022232"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007406","name":"Fundaci\u00f3n BBVA","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007406","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2025,8,7]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain nonasymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings.<\/jats:p>","DOI":"10.1137\/24m1629328","type":"journal-article","created":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T07:16:50Z","timestamp":1754551010000},"page":"543-575","source":"Crossref","is-referenced-by-count":2,"title":["Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint"],"prefix":"10.1137","volume":"67","author":[{"given":"Daniel","family":"Sanz-Alonso","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Chicago, Chicago, IL 60637 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1731-6151","authenticated-orcid":true,"given":"Nathan","family":"Waniorek","sequence":"additional","affiliation":[{"name":"Committee on Computational and Applied Mathematics, University of Chicago, Chicago, IL 60637 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,8,7]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2021.04.001"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-015-9276-6"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1214\/17-STS611"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1214\/12-AOS1032"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/21M146209X"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.3150\/24-BEJ1809"},{"key":"ref7","first-page":"1179","volume":"9","author":"Bach F. R.","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/26\/3\/035010"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492918000016"},{"key":"ref11","first-page":"4313","volume":"367","author":"Bickel P. J.","year":"2009","journal-title":"Philos. Trans. Roy. Soc. Lond. Ser. A Math. Phys. Eng. Sci."},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOS620"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ad2696"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcmds.2024.100094"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1561\/2200000016"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-024-01439-2"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20192-9"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1137\/12089586X"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.4171\/8ecm\/01"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1137\/080723995"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/31\/12\/125005"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/15M1055061"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/20M1326246"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab4d92"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-23824-6"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/23M1564043"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aaf5ab"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1145\/2184319.2184343"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-012-0540-0"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.10116"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2010.10.002"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-012-9135-7"},{"key":"ref33","unstructured":"V. Chen, M. M. Dunlop, O. Papaspiliopoulos, and A. M. Stuart, Dimension-Robust MCMC in Bayesian Inverse Problems, preprint, arXiv:1803.03344, 2018."},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1214\/13-STS421"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/79.974718"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/18.382009"},{"key":"ref37","unstructured":"D. L. Donoho, High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality, Lecture delivered at the AMS \u201cMathematical Challenges of the 21st Century\u201d Conference, Los Angeles, 2000."},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.5802\/smai-jcm.62"},{"key":"ref39","first-page":"1022","volume":"21","author":"Trillos N. Garc\u00eda","year":"2020","journal-title":"J. Mach. Learn. Res."},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1201\/9781420072884"},{"key":"ref41","author":"Gelman A.","year":"1995","journal-title":"Chapman and Hall\/CRC"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1137\/23M156255X"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20350"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9574.1992.tb01335.x"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS778"},{"key":"ref46","unstructured":"P. J. Huber, The behavior of maximum likelihood estimation under nonstandard conditions, in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, L. M. LeCam and J. Neyman, eds. University of California Press, 1967, pp. 221\u2013233."},{"key":"ref47","doi-asserted-by":"crossref","unstructured":"L. Jacob, G. Obozinski, and J.P. Vert, Group Lasso with overlap and graph Lasso, in Proceedings of the 26th Annual International Conference on Machine Learning, ACM, 2009, pp. 433\u2013440.","DOI":"10.1145\/1553374.1553431"},{"key":"ref48","volume-title":"Appl. Math. Sci","volume":"160","author":"Kaipio J.","year":"2006"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.3934\/fods.2023003"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-20325-6"},{"key":"ref51","first-page":"559","volume":"16","author":"Loh P.-L.","year":"2015","journal-title":"J. Mach. Learn. Res."},{"key":"ref52","unstructured":"K. Lounici, M. Pontil, A. Tsybakov, and S. Van De Geer, Taking advantage of sparsity in multi-task learning, in 22nd Conference on Learning Theory (COLT 2009), 2009, pp. 73\u201382."},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2007.914728"},{"key":"ref54","volume-title":"A Wavelet Tour of Signal Processing","author":"Mallat S.","year":"1999"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1214\/07-AOS582"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1214\/12-STS400"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1214\/12-STS400"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1198\/016214508000000337"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2021039"},{"key":"ref60","first-page":"2241","volume":"11","author":"Raskutti G.","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2165799"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1137\/070697835"},{"key":"ref63","unstructured":"J. A. Reeds, On the Definition of von Mises Functionals, Ph.D. thesis, Harvard University, 1976."},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1996.3079"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1017\/9781009414319"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1137\/23M1567035"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.3150\/21-BEJ1336"},{"key":"ref68","doi-asserted-by":"publisher","DOI":"10.1137\/22M153330X"},{"key":"ref69","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492910000061"},{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1996.tb02080.x"},{"key":"ref71","series-title":"Camb. Ser. Stat. Probab. Math. 6","volume-title":"Empirical Processes in M-Estimation","author":"van de Geer S.","year":"2000"},{"key":"ref72","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000929"},{"key":"ref73","doi-asserted-by":"publisher","DOI":"10.1111\/sjos.12032"},{"key":"ref74","doi-asserted-by":"publisher","DOI":"10.1017\/9781108627771"},{"key":"ref75","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4815-2"},{"key":"ref76","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/acad21"},{"key":"ref77","doi-asserted-by":"publisher","DOI":"10.1198\/jcgs.2011.203main"},{"key":"ref78","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2005.00532.x"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M1629328","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:29:22Z","timestamp":1787228962000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1629328"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,7]]},"references-count":78,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,8,7]]}},"alternative-id":["10.1137\/24M1629328"],"URL":"https:\/\/doi.org\/10.1137\/24m1629328","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,7]]}}}