Random forward models and log-likelihoods in Bayesian inverse problems

Please always quote using this URN: urn:nbn:de:0297-zib-66324
  • 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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Metadaten
Author:Han Cheng Lie, Tim Sullivan, Aretha Teckentrup
Document Type:Article
Parent Title (English):SIAM/ASA Journal on Uncertainty Quantification
Volume:6
Issue:4
First Page:1600
Last Page:1629
Tag:Bayesian inverse problem; posterior consistency; probabilistic numerics; random likelihood; randomised misfit; surrogate model; uncertainty quantification
MSC-Classification:62-XX STATISTICS
65-XX NUMERICAL ANALYSIS
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)
Date of first Publication:2018/01/04
Series (Serial Number):ZIB-Report (18-03)
ArXiv Id:http://arxiv.org/abs/1712.05717
ISSN:1438-0064
DOI:https://doi.org/10.1137/18M1166523