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Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals

Author(s)
Marzouk, Youssef M
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Abstract
In this article we develop a new sequential Monte Carlo method for multilevel Monte Carlo estimation. In particular, the method can be used to estimate expectations with respect to a target probability distribution over an infinite-dimensional and noncompact space—as produced, for example, by a Bayesian inverse problem with a Gaussian random field prior. Under suitable assumptions the MLSMC method has the optimal O(ε−2) bound on the cost to obtain a mean-square error of O(ε2). The algorithm is accelerated by dimension-independent likelihood-informed proposals [T. Cui, K. J. Law, and Y. M. Marzouk, (2016), J. Comput. Phys., 304, pp. 109–137] designed for Gaussian priors, leveraging a novel variation which uses empirical covariance information in lieu of Hessian information, hence eliminating the requirement for gradient evaluations. The efficiency of the algorithm is illustrated on two examples: (i) inversion of noisy pressure measurements in a PDE model of Darcy flow to recover the posterior distribution of the permeability field and (ii) inversion of noisy measurements of the solution of an SDE to recover the posterior path measure.
Date issued
2018-06
URI
https://hdl.handle.net/1721.1/126540
Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Journal
SIAM/ASA journal on uncertainty quantification
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Beskos, Alexandros et al. “Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals.” SIAM/ASA journal on uncertainty quantification, vol. 6, no. 2, 2018, pp. 762-786 © 2018 The Author(s)
Version: Final published version
ISSN
2166-2525

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