UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

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

Beskos, A; Jasra, A; Law, K; Marzouk, Y; Zhou, Y; (2018) Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals. SIAM-ASA Journal on Uncertainty Quantification , 6 (2) pp. 762-786. 10.1137/17M1120993. Green open access

[img]
Preview
Text
Beskos et al_17m1120993.pdf - Published version

Download (581kB) | Preview

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(ε 2 ). 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.

Type: Article
Title: Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals
Open access status: An open access version is available from UCL Discovery
DOI: 10.1137/17M1120993
Publisher version: https://doi.org/10.1137/17M1120993
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: multilevel Monte Carlo, sequential Monte Carlo, Bayesian inverse problem, uncertainty quantification
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1556084
Downloads since deposit
31Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item