{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T11:04:06Z","timestamp":1779879846794,"version":"3.53.1"},"reference-count":48,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100006227","name":"Lawrence Livermore National Laboratory","doi-asserted-by":"publisher","award":["DE-AC52-07NA27344"],"award-info":[{"award-number":["DE-AC52-07NA27344"]}],"id":[{"id":"10.13039\/100006227","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM\/ASA J. Uncertainty Quantification"],"published-print":{"date-parts":[[2026,6,30]]},"DOI":"10.1137\/25m179590x","type":"journal-article","created":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T10:22:11Z","timestamp":1779877331000},"page":"597-620","source":"Crossref","is-referenced-by-count":0,"title":["Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen\u2013Lo\u00e8ve Decomposition"],"prefix":"10.1137","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6882-9737","authenticated-orcid":true,"given":"Sohail","family":"Reddy","sequence":"first","affiliation":[{"name":"Corresponding author. Lawrence Livermore National Laboratory, Livermore, CA 94550 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,5,27]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2008.01.012"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1086\/311042"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.compgeo.2023.105304"},{"key":"ref4","volume-title":"Markov Chain Monte Carlo Methods: Survey with Some Frequent Misunderstandings","author":"Robert C. P.","year":"2021"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-65723-8_32"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.compgeo.2022.104783"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2017.05.022"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2011.08.002"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-008-0018-3"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-7152(98)00209-0"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/17M1149730"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2011.00777.x"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2024.117146"},{"key":"ref14","doi-asserted-by":"crossref","unstructured":"L. M. Paun, M. Colebank, M. U. Qureshi, M. Olufsen, N. Hill, and D. Husmeier, MCMC with delayed acceptance using a surrogate model with an application to cardiovascular fluid dynamics, in Proceedings of the International Conference on Statistics: Theory and Applications, Lisbon, Portugal, 2019, ICSTA 28.","DOI":"10.11159\/icsta19.28"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2023.109059"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/20M1315774"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2020.107008"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.OA-2020-0186"},{"key":"ref19","unstructured":"H. J. Hortua, R. Volpi, D. Marinelli, and L. Malago, Accelerating MCMC algorithms through Bayesian deep networks, in Proceedings of the 34th Conference on Neural Information Processing Systems, Canada, 2020."},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1002\/wics.1435"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-024-10187-8"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/16M1082688"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/18M1175239"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1137\/20M1329044"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/130915005"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/19M126966X"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1137\/20M1349606"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1137\/110853054"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-013-0546-4"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1017\/apr.2018.49"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatfluidflow.2009.06.006"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1017\/jfm.2018.954"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1029\/2020EA001321"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/978-90-481-3520-2"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/22M1476770"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2021.113895"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-011-0160-x"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1137\/100800531"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2019.1665537"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/dry091"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2015-02937-8"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-018-1241-0"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2017.1285773"},{"key":"ref44","volume-title":"Reversibility and Stochastic Networks","author":"Kelly F. P.","year":"1979"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/adb52a"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/528281"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.01.048"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.2514\/1.J058809"}],"container-title":["SIAM\/ASA Journal on Uncertainty Quantification"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T10:22:13Z","timestamp":1779877333000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/25M179590X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,27]]},"references-count":48,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,6,30]]}},"alternative-id":["10.1137\/25M179590X"],"URL":"https:\/\/doi.org\/10.1137\/25m179590x","relation":{},"ISSN":["2166-2525"],"issn-type":[{"value":"2166-2525","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,27]]}}}