2017/03/15 by Alexandros Beskos, Ajay Jasra, Beskos, Alexandros +8 · 2 citations
Engineering · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Nuclear reactor physics and engineering #Statistical Methods and Inference #stat.CO
paper · pdf · doi:10.48550/arxiv.1703.04866
arxiv created 2017/03/15 · openalex publication_date 2017/03/15 · arxiv updated 2017/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we develop a new sequential Monte Carlo (SMC) method for multilevel (ML) 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 non-compact space as given, for example, by a Bayesian inverse problem with 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 (DILI) proposals designed for Gaussian priors, leveraging a novel variation which uses empirical sample covariance information in lieu of Hessian information, hence eliminating the requirement for gradient evaluations. The efficiency of the algorithm is illustrated on two examples: inversion of noisy pressure measurements in a PDE model of Darcy flow to recover the posterior distribution of the permeability field, and inversion of noisy measurements of the solution of an SDE to recover the posterior path measure.