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Random forward models and log-likelihoods in Bayesian inverse problems

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Lie, H. C., Sullivan, T. J. and Teckentrup, A. L. (2018) Random forward models and log-likelihoods in Bayesian inverse problems. SIAM/ASA Journal on Uncertainty Quantification, 6 (4). pp. 1600-1629. doi:10.1137/18M1166523 ISSN 2166-2525.

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Official URL: http://dx.doi.org/10.1137/18M1166523

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Abstract

We consider the use of randomized forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive model is approximated using a cheaper stochastic surrogate, as in Gaussian process emulation (kriging) or in the field of probabilistic numerical methods. We show that the Hellinger distance between the exact and approximate Bayesian posteriors is bounded by moments of the difference between the true and approximate log-likelihoods. Example applications of these stability results are given for randomized misfit models in large data applications and the probabilistic solution of ordinary differential equations.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Divisions: Faculty of Science, Engineering and Medicine > Engineering > Engineering
Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Bayesian statistical decision theory, Gaussian processes, Probabilities, Differential equations
Journal or Publication Title: SIAM/ASA Journal on Uncertainty Quantification
Publisher: Society for Industrial and Applied Mathematics
ISSN: 2166-2525
Official Date: 15 November 2018
Dates:
DateEvent
15 November 2018Published
21 September 2018Accepted
Volume: 6
Number: 4
Page Range: pp. 1600-1629
DOI: 10.1137/18M1166523
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: © 2018, Society for Industrial and Applied Mathematics
Date of first compliant deposit: 15 April 2020
Date of first compliant Open Access: 15 April 2020
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/N510129/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
UNSPECIFIED[DFG] Deutsche Forschungsgemeinschafthttp://dx.doi.org/10.13039/501100001659
CRC 1114[DFG] Deutsche Forschungsgemeinschafthttp://dx.doi.org/10.13039/501100001659
DMS-1127914National Science Foundationhttp://dx.doi.org/10.13039/501100008982

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