Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals
Name
17m1120993.pdf
Description
Published version
Size
568.32 KB
Format
Adobe PDF
Checksum (MD5)
9b43d06f0db907b30cb6fa3692153916
Author(s)
Marzouk, Youssef M
Date Issued
June 2018
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/17M1120993
