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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
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Official URL: http://dx.doi.org/10.1137/18M1166523
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 | |||||||||||||||
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| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| 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: |
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| 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 | |||||||||||||||
| RIOXX Funder/Project Grant: |
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