Work

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

Year: 2017

Type: article

Abstract: This article considers the Sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic Partial Differential Equations (PDEs). The examples involve the inversion of observations of the solution of (i) a one-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a two-dimensional Poisson equation to infer the external forcing.

Source: ACM Transactions on Modeling and Computer Simulation

DOI: 10.1145/3092841

Authors: Pierre Del Moral, Ajay Jasra, Kody J. H. Law, Yan Zhou

Institutions: Institut national de recherche en sciences et technologies du numérique, Centre Inria de l'université de Bordeaux, National University of Singapore, Oak Ridge National Laboratory, BGI Group (China)

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Defense Advanced Research Projects Agency, Laboratory Directed Research and Development, Oak Ridge National Laboratory

OpenAlex ID: W2963868836

FWCI: 2.419

Cites: 31

Cited by: 25

Related to: 10