Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

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

doi:10.1145/3092841

Title: Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

Journal Article · Thu Aug 24 00:00:00 EDT 2017 · ACM Transactions on Modeling and Computer Simulation

DOI:https://doi.org/10.1145/3092841· OSTI ID:1393885

Moral, Pierre Del ^[1]; Jasra, Ajay ^[2];

^[3]; Zhou, Yan ^[2]

Univ. Bordeaux (France). Center INRIA Bordeaux Sud-Ouest & Institut de Mathematiques de Bordeaux
National Univ. of Singapore (Singapore). Dept. of Statistics & Applied Probability
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Div.

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 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional Poisson equation to infer the external forcing.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1393885

Journal Information:: ACM Transactions on Modeling and Computer Simulation, Vol. 27, Issue 3; ISSN 1049-3301

Publisher:: Association for Computing MachineryCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 15 works

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Cited By (3)

On coupling particle filter trajectories Sen, Deborshee; Thiery, Alexandre H.; Jasra, Ajay Statistics and Computing, Vol. 28, Issue 2 https://doi.org/10.1007/s11222-017-9740-z	journal	March 2017
On Coupling Particle Filter Trajectories Sen, Deborshee; Thiery, Alexandre; Jasra, Ajay arXiv https://doi.org/10.48550/arxiv.1606.01016	preprint	January 2016
Multilevel Sequential Monte Carlo with Dimension-Independent Likelihood-Informed Proposals Beskos, Alexandros; Jasra, Ajay; Law, Kody arXiv https://doi.org/10.48550/arxiv.1703.04866	preprint	January 2017

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