Multilevel Sequential Monte Carlo Samplers for Normalizing Constants
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 1dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2dimensional Poisson equation to infer the external forcing.
 Authors:

^{[1]};
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;
^{[2]}
 Univ. Bordeaux (France). Center INRIA Bordeaux SudOuest & 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.
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 ACM Transactions on Modeling and Computer Simulation
 Additional Journal Information:
 Journal Volume: 27; Journal Issue: 3; Journal ID: ISSN 10493301
 Publisher:
 Association for Computing Machinery
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1393885
Moral, Pierre Del, Jasra, Ajay, Law, Kody J. H., and Zhou, Yan. Multilevel Sequential Monte Carlo Samplers for Normalizing Constants. United States: N. p.,
Web. doi:10.1145/3092841.
Moral, Pierre Del, Jasra, Ajay, Law, Kody J. H., & Zhou, Yan. Multilevel Sequential Monte Carlo Samplers for Normalizing Constants. United States. doi:10.1145/3092841.
Moral, Pierre Del, Jasra, Ajay, Law, Kody J. H., and Zhou, Yan. 2017.
"Multilevel Sequential Monte Carlo Samplers for Normalizing Constants". United States.
doi:10.1145/3092841. https://www.osti.gov/servlets/purl/1393885.
@article{osti_1393885,
title = {Multilevel Sequential Monte Carlo Samplers for Normalizing Constants},
author = {Moral, Pierre Del and Jasra, Ajay and Law, Kody J. H. and Zhou, Yan},
abstractNote = {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 1dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2dimensional Poisson equation to infer the external forcing.},
doi = {10.1145/3092841},
journal = {ACM Transactions on Modeling and Computer Simulation},
number = 3,
volume = 27,
place = {United States},
year = {2017},
month = {8}
}