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Abstract
We are interested in computing the expectation of a functional of a PDE solution under a Bayesian posterior distribution. Using Bayes's rule, we reduce the problem to estimating the ratio of two related prior expectations. For a model elliptic problem, we provide a full convergence and complexity analysis of the ratio estimator in the case where Monte Carlo, quasiMonte Carlo, or multilevel Monte Carlo methods are used as estimators for the two prior expectations. We show that the computational complexity of the ratio estimator to achieve a given accuracy is the same as the corresponding complexity of the individual estimators for the numerator and the denominator. We also include numerical simulations, in the context of the model elliptic problem, which demonstrate the effectiveness of the approach.
Original language  English 

Pages (fromto)  493518 
Number of pages  26 
Journal  SIAM/ASA Journal on Uncertainty Quantification 
Volume  5 
Issue number  1 
Early online date  27 Apr 2017 
DOIs  
Publication status  Published  31 Dec 2017 
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Dive into the research topics of 'QuasiMonte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems'. Together they form a unique fingerprint.Projects
 2 Finished

Multiscale Modelling of Aerospace Composites
Butler, R. & Scheichl, R.
Engineering and Physical Sciences Research Council
6/01/14 → 5/02/18
Project: Research council

Multilevel Monte Carlo Methods for Elliptic Problems
Scheichl, R.
Engineering and Physical Sciences Research Council
1/07/11 → 30/06/14
Project: Research council