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Random forward models and log-likelihoods in Bayesian inverse problems

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Original languageEnglish
Pages (from-to)1600–1629
JournalSIAM/ASA Journal on Uncertainty Quantification
Issue number4
Early online date15 Nov 2018
Publication statusPublished - 15 Nov 2018


We consider the use of randomised 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 randomised misfit models in large data applications and the probabilistic solution of ordinary differential equations.

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