A posteriori stochastic correction of reduced models in delayed acceptance MCMC, with application to multiphase subsurface inverse problems

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dc.contributor.author Cui, T en
dc.contributor.author Fox, C en
dc.contributor.author O'Sullivan, Michael en
dc.date.accessioned 2019-06-19T01:52:51Z en
dc.date.issued 2019-06-08 en
dc.identifier.citation International Journal for Numerical Methods in Engineering 118(10):578-605 08 Jun 2019 en
dc.identifier.issn 0029-5981 en
dc.identifier.uri http://hdl.handle.net/2292/47186 en
dc.description.abstract Sample‐based Bayesian inference provides a route to uncertainty quantification in the geosciences and inverse problems in general but is very computationally demanding in the naïve form, which requires simulating an accurate computer model at each iteration. We present a new approach that constructs a stochastic correction to the error induced by a reduced model, with the correction improving as the algorithm proceeds. This enables sampling from the correct target distribution at reduced computational cost per iteration, as in existing delayed‐acceptance schemes, while avoiding appreciable loss of statistical efficiency that necessarily occurs when using a reduced model. Use of the stochastic correction significantly reduces the computational cost of estimating quantities of interest within desired uncertainty bounds. In contrast, existing schemes that use a reduced model directly as a surrogate do not actually improve computational efficiency in our target applications. We build on recent simplified conditions for adaptive Markov chain Monte Carlo algorithms to give practical approximation schemes and algorithms with guaranteed convergence. The efficacy of this new approach is demonstrated in two computational examples, including calibration of a large‐scale numerical model of a real geothermal reservoir, that show good computational and statistical efficiencies on both synthetic and measured data sets. en
dc.publisher Wiley en
dc.relation.ispartofseries International Journal for Numerical Methods in Engineering en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights This is the peer reviewed version of the following article:International Journal for Numerical Methods in Engineering 118(10):578-605 08 Jun 2019, which has been published in final form at http://dx.doi.org/10.1002/nme.6028. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.rights.uri https://authorservices.wiley.com/author-resources/Journal-Authors/licensing/self-archiving.html en
dc.title A posteriori stochastic correction of reduced models in delayed acceptance MCMC, with application to multiphase subsurface inverse problems en
dc.type Journal Article en
dc.identifier.doi 10.1002/nme.6028 en
pubs.issue 10 en
pubs.begin-page 578 en
pubs.volume 118 en
dc.rights.holder Copyright: John Wiley & Sons, Ltd. en
pubs.end-page 605 en
pubs.publication-status Published en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en
pubs.subtype Article en
pubs.elements-id 764319 en
pubs.org-id Engineering en
pubs.org-id Engineering Science en
pubs.record-created-at-source-date 2019-03-01 en


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