Incorporating posterior model discrepancy into a hierarchical framework to facilitate out-of-the-box MCMC sampling for geothermal inverse problems and uncertainty quantification

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dc.contributor.author MacLaren, Oliver en
dc.contributor.author Nicholson, R en
dc.contributor.author Bjarkason, Elvar en
dc.contributor.author O'Sullivan, Michael en
dc.date.accessioned 2019-02-28T00:08:53Z en
dc.date.issued 2018-10-10 en
dc.identifier.uri http://hdl.handle.net/2292/45613 en
dc.description.abstract We consider geothermal inverse problems and uncertainty quantification from a Bayesian perspective. Our goal is to make standard, 'out-of-the-box' Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models. To do this, we first show how to pose the inverse and prediction problems in a hierarchical Bayesian framework. We then show how to incorporate so-called posterior model approximation error into this hierarchical framework, using a modified form of the Bayesian approximation error (BAE) approach. This enables the use of a 'coarse', approximate model in place of a finer, more expensive model, while also accounting for the additional uncertainty and potential bias that this can introduce. Our method requires only simple probability modelling and only modifies the target posterior - the same standard MCMC sampling algorithm can be used to sample the new target posterior. We show that our approach can achieve significant computational speed-ups on a geothermal test problem. A problem which would take around a year to carry out full MCMC sampling for, now only takes around a day or so using our approach. We also demonstrate the dangers of naively using coarse, approximate models in place of finer models, without accounting for model discrepancies. The naive approach tends to give overly confident and biased posteriors, while incorporating BAE into our hierarchical framework corrects for this while maintaining computational efficiency and ease-of-use. en
dc.relation.ispartof Arvix 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.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.subject stat.CO en
dc.subject stat.CO en
dc.subject math.NA en
dc.title Incorporating posterior model discrepancy into a hierarchical framework to facilitate out-of-the-box MCMC sampling for geothermal inverse problems and uncertainty quantification en
dc.type Report en
dc.rights.holder Copyright: The author en
pubs.author-url http://arxiv.org/abs/1810.04350v1 en
dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en
pubs.subtype Working Paper en
pubs.elements-id 754738 en
pubs.org-id Engineering en
pubs.org-id Engineering Science en
pubs.arxiv-id 1810.04350 en
pubs.number 1810.04350v1 en
pubs.record-created-at-source-date 2019-07-29 en


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