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Title: Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

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

Authors:
 [1];  [2]; ORCiD logo [3];  [2]
  1. Univ. Bordeaux (France). Center INRIA Bordeaux Sud-Ouest & Institut de Mathematiques de Bordeaux
  2. National Univ. of Singapore (Singapore). Dept. of Statistics & Applied Probability
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Div.
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1393885
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
ACM Transactions on Modeling and Computer Simulation
Additional Journal Information:
Journal Volume: 27; Journal Issue: 3; Journal ID: ISSN 1049-3301
Publisher:
Association for Computing Machinery
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Moral, Pierre Del, Jasra, Ajay, Law, Kody J. H., and Zhou, Yan. Multilevel Sequential Monte Carlo Samplers for Normalizing Constants. United States: N. p., 2017. Web. https://doi.org/10.1145/3092841.
Moral, Pierre Del, Jasra, Ajay, Law, Kody J. H., & Zhou, Yan. Multilevel Sequential Monte Carlo Samplers for Normalizing Constants. United States. https://doi.org/10.1145/3092841
Moral, Pierre Del, Jasra, Ajay, Law, Kody J. H., and Zhou, Yan. Thu . "Multilevel Sequential Monte Carlo Samplers for Normalizing Constants". United States. https://doi.org/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 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional 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}
}

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