On solving integral equations using Markov chain Monte Carlo methods

A Doucet, AM Johansen, VB Tadic

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)

Abstract

In this paper, we propose an original approach to the solution of Fredholm equations of the second kind. We interpret the standard Von Neumann expansion of the solution as an expectation with respect to a probability distribution defined on a union of subspaces of variable dimension. Based on this representation, it is possible to use trans-dimensional Markov chain Monte Carlo (MCMC) methods such as Reversible Jump MCMC to approximate the solution numerically. This can be an attractive alternative to standard Sequential Importance Sampling (SIS) methods routinely used in this context. To motivate our approach, we sketch an application to value function estimation for a Markov decision process. Two computational examples are also provided.
Translated title of the contributionOn solving integral equations using Markov chain Monte Carlo methods
Original languageEnglish
Pages (from-to)2869 - 2880
Number of pages12
JournalApplied Mathematics and Computation
Volume216
Issue number10
DOIs
Publication statusPublished - 15 Jul 2010

Bibliographical note

Publisher: Elsevier

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