6632
eng
1600
1629
4
6
article
0
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2018-01-04
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Random forward models and log-likelihoods in Bayesian inverse problems
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.
SIAM/ASA Journal on Uncertainty Quantification
1438-0064
urn:nbn:de:0297-zib-66324
1712.05717
10.1137/18M1166523
2018
yes
Han Cheng Lie
Tim Sullivan
T. J. Sullivan
Aretha Teckentrup
ZIB-Report
18-03
eng
uncontrolled
Bayesian inverse problem
eng
uncontrolled
random likelihood
eng
uncontrolled
surrogate model
eng
uncontrolled
posterior consistency
eng
uncontrolled
probabilistic numerics
eng
uncontrolled
uncertainty quantification
eng
uncontrolled
randomised misfit
STATISTICS
NUMERICAL ANALYSIS
COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)
Numerical Mathematics
Sullivan, Tim
SFB1114 A06
https://opus4.kobv.de/opus4-zib/files/6632/random-bip.pdf