{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:41Z","timestamp":1787337221862,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>We study the preconditioning of Markov chain Monte Carlo (MCMC) methods using coarse-scale models with applications to subsurface characterization. The purpose of preconditioning is to reduce the fine-scale computational cost and increase the acceptance rate in the MCMC sampling. This goal is achieved by generating Markov chains based on two-stage computations. In the first stage, a new proposal is first tested by the coarse-scale model based on multiscale finite volume methods. The full fine-scale computation will be conducted only if the proposal passes the coarse-scale screening. For more efficient simulations, an approximation of the full fine-scale computation using precomputed multiscale basis functions can also be used. Comparing with the regular MCMC method, the preconditioned MCMC method generates a modified Markov chain by incorporating the coarse-scale information of the problem. The conditions under which the modified Markov chain will converge to the correct posterior distribution are stated in the paper. The validity of these assumptions for our application and the conditions which would guarantee a high acceptance rate are also discussed. We would like to note that coarse-scale models used in the simulations need to be inexpensive but not necessarily very accurate, as our analysis and numerical simulations demonstrate. We present numerical examples for sampling permeability fields using two-point geostatistics. The Karhunen--Lo\u00e8ve expansion is used to represent the realizations of the permeability field conditioned to the dynamic data, such as production data, as well as some static data. Our numerical examples show that the acceptance rate can be increased by more than 10 times if MCMC simulations are preconditioned using coarse-scale models.<\/jats:p>","DOI":"10.1137\/050628568","type":"journal-article","created":{"date-parts":[[2008,2,6]],"date-time":"2008-02-06T16:45:19Z","timestamp":1202316319000},"page":"776-803","source":"Crossref","is-referenced-by-count":143,"title":["Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models"],"prefix":"10.1137","volume":"28","author":[{"given":"Y.","family":"Efendiev","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T.","family":"Hou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"W.","family":"Luo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/030600655"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1198\/106186005X76983"},{"key":"R3","unstructured":"P. Dostert, Y. Efendiev, T. Hou, and W. Luo,\n                      Coarse\u2010gradient Langevin algorithms for dynamic data integration and uncertainty quantification\n                      , J. Comput. Phys., to appear."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1029\/91WR00107"},{"key":"R5","unstructured":"Y. Efendiev, A. Datta\u2010Gupta, V. Ginting, X. Ma, and B. Mallick,\n                      An efficient two\u2010stage Markov chain Monte Carlo method for dynamic data integration\n                      , Water Resour. Res., W12423."},{"key":"R6","unstructured":"Y. Efendiev, V. Ginting, T. Hou, and R. Ewing,\n                      Accurate multiscale finite element methods for two\u2010phase flow simulations\n                      , J. Comput. Phys., to appear."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1515\/156939504323074513"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2004.04.008"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(99)00103-7"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1109\/78.978393"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1997.5682"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9991(03)00075-5"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/030600795"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1029\/95WR01945"},{"key":"R15","unstructured":"J. S. Liu,\n                      Monte Carlo Strategies in Scientific Computing\n                      , Springer, New York, 2001."},{"key":"R16","doi-asserted-by":"crossref","unstructured":"O. Lodoen, H. Omre, L. Durlofsky, and Y. Chen,\n                      Assessment of uncertainty in reservoir production forecasts using upscaled models\n                      , in Proceedings of the Seventh International Geostatistics Congress, Banff, AB, Canada, 2004.","DOI":"10.1007\/978-1-4020-3610-1_72"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"M. Loeve,\n                      Probability Theory\n                      , 4th ed., Springer, Berlin, 1977.","DOI":"10.1007\/978-1-4684-9464-8_1"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-3267-7"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1007\/BF02769620"},{"key":"R20","doi-asserted-by":"crossref","unstructured":"D. Oliver, N. He, and A. Reynolds,\n                      Conditioning permeability fields to pressure data\n                      , in Proceedings of the 5th European Conference on the Mathematics of Oil Recovery, Leoben, Austria, 1996.","DOI":"10.3997\/2214-4609.201406884"},{"key":"R21","doi-asserted-by":"crossref","unstructured":"H. Omre and O. P. Lodoen,\n                      Improved production forecasts and history matching using approximate fluid\u2010flow simulators\n                      , SPE Journal, (2004), pp. 339\u2013351.","DOI":"10.2118\/74691-PA"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4145-2"},{"key":"R23","unstructured":"Eugene Wong, Procesy stochastyczne w teorii informacji i uk\u0142adach dynamicznych, Wydawnictwa Naukowo\u2010Techniczne, Warsaw, 1976, 292\u20130, Translated from the English by Krzysztof Nowak54:3778"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050628568","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:19Z","timestamp":1787334619000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050628568"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/050628568"],"URL":"https:\/\/doi.org\/10.1137\/050628568","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}