dc.contributor.author Dodwell, T dc.contributor.author Ketelsen, C dc.contributor.author Scheichl, R dc.contributor.author Teckentrup, A dc.date.accessioned 2019-08-12T07:33:35Z dc.date.issued 2019-08-12 dc.description.abstract In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large-scale applications with high-dimensional parameter spaces, e.g., in uncertainty quantification in porous media flow. We propose a new multilevel Metropolis--Hastings algorithm and give an abstract, problem-dependent theorem on the cost of the new multilevel estimator based on a set of simple, verifiable assumptions. For a typical model problem in subsurface flow, we then provide a detailed analysis of these assumptions and show significant gains over the standard Metropolis--Hastings estimator. Numerical experiments confirm the analysis and demonstrate the effectiveness of the method with consistent reductions of more than an order of magnitude in the cost of the multilevel estimator over the standard Metropolis--Hastings algorithm for tolerances $\varepsilon < 10^{-2}$. en_GB dc.description.sponsorship Alan Turing Institute en_GB dc.identifier.citation Vol. 61 (3), pp.509–545. en_GB dc.identifier.doi https://doi.org/10.1137/19M126966X dc.identifier.uri http://hdl.handle.net/10871/38300 dc.language.iso en en_GB dc.publisher Society for Industrial and Applied Mathematics en_GB dc.rights (C) 2019 Society for Industrial and Applied Mathematics en_GB dc.title Multilevel Markov Chain Monte Carlo en_GB dc.type Article en_GB dc.date.available 2019-08-12T07:33:35Z dc.identifier.issn 0036-1445 dc.description This is the author accepted manuscript. The final version is available from Society for Industrial and Applied Mathematics via the DOI in this record. en_GB dc.identifier.journal SIAM Review en_GB dc.rights.uri http://www.rioxx.net/licenses/all-rights-reserved en_GB dcterms.dateAccepted 2019-08-07 exeter.funder ::Alan Turing Institute en_GB rioxxterms.version AM en_GB rioxxterms.licenseref.startdate 2019-08-07 rioxxterms.type Journal Article/Review en_GB refterms.dateFCD 2019-08-11T17:22:33Z refterms.versionFCD AM refterms.dateFOA 2019-08-12T07:33:38Z refterms.panel B en_GB
﻿