{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:24:10Z","timestamp":1787340250243,"version":"3.56.0"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301337"],"award-info":[{"award-number":["11301337"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM\/ASA J. Uncertainty Quantification"],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>The preconditioned Crank--Nicolson (pCN) method is a Markov chain Monte Carlo (MCMC) scheme, specifically designed to perform Bayesian inferences in function spaces. Unlike many standard MCMC algorithms, the pCN method can preserve the sampling efficiency under the mesh refinement, a property referred to as being dimension independent. In this work we consider an adaptive strategy to further improve the efficiency of pCN. In particular we develop a hybrid adaptive MCMC method: the algorithm performs an adaptive Metropolis scheme in a chosen finite dimensional subspace and a standard pCN algorithm in the complement space of the chosen subspace. We show that the proposed algorithm satisfies certain important ergodicity conditions. Finally with numerical examples we demonstrate that the proposed method has competitive performance with existing adaptive algorithms.<\/jats:p>","DOI":"10.1137\/16m1082950","type":"journal-article","created":{"date-parts":[[2017,7,12]],"date-time":"2017-07-12T10:32:45Z","timestamp":1499855565000},"page":"621-639","source":"Crossref","is-referenced-by-count":7,"title":["A Hybrid Adaptive MCMC Algorithm in Function Spaces"],"prefix":"10.1137","volume":"5","author":[{"given":"Qingping","family":"Zhou","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zixi","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhewei","family":"Yao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinglai","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,7,12]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-008-9110-y"},{"key":"atypb2","first-page":"32","author":"Atchade Y.","year":"2011","journal-title":"Cambridge"},{"key":"atypb3","unstructured":"Y. Bai, G. O. Roberts, and J. S. Rosenthal,\n                      On the Containment Condition for Adaptive Markov Chain Monte Carlo Algorithms\n                      ,http:\/\/probability.ca\/jeff\/ftpdir\/yanbai1.pdf(2009)."},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/15M1026432"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1214\/13-STS421"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.10.008"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1002\/nme.4748"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"G. Da Prato,\n                      An introduction to Infinite-Dimensional Analysis\n                      , Springer, New York, 2006.","DOI":"10.1007\/3-540-29021-4"},{"key":"atypb9","unstructured":"Z. Feng and J. Li,\n                      An Adaptive Independence Sampler MCMC Algorithm for Infinite Dimensional Bayesian Inferences\n                      , preprint 1508.03283, 2015."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.2307\/3318737"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.11.024"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"J. Kaipio and E. Somersalo,\n                      Statistical and Computational Inverse Problems\n                      , Vol. 160, Springer, New York, 2006.","DOI":"10.1007\/b138659"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1080\/00031305.1998.10480547"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2013.07.026"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/130938189"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1214\/10-AAP754"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"C. E. Rasmussen,\n                      Gaussian Processes for Machine Learning\n                      , MIT Press, Cambridge, MA, 2006.","DOI":"10.7551\/mitpress\/3206.001.0001"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"C. Robert and G. Casella,\n                      Monte Carlo Statistical Methods\n                      , 2nd ed., Springer, New York, 2004.","DOI":"10.1007\/978-1-4757-4145-2"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1198\/jcgs.2009.06134"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1015346320"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1183667414"},{"key":"atypb22","unstructured":"D. Rudolf and B. Sprungk,\n                      On a generalization of the preconditioned Crank-Nicolson Metropolis algorithm\n                      , Found. Comput. Math. (2015), pp. 1-35."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492910000061"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1137\/140965144"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2507"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/32\/7\/075006"}],"container-title":["SIAM\/ASA Journal on Uncertainty Quantification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1082950","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:26:53Z","timestamp":1787336813000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1082950"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1082950"],"URL":"https:\/\/doi.org\/10.1137\/16m1082950","relation":{},"ISSN":["2166-2525"],"issn-type":[{"value":"2166-2525","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}