Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems

@article{Scheichl2017QuasiMonteCA,
  title={Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems},
  author={Robert Scheichl and Andrew M. Stuart and Aretha L. Teckentrup},
  journal={SIAM/ASA J. Uncertain. Quantification},
  year={2017},
  volume={5},
  pages={493-518}
}
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, quasi-Monte Carlo, or multilevel Monte Carlo methods are used as estimators for the two prior expectations. We show that the computational… Expand
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