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On solving integral equations using Markov chain Monte Carlo methods
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Doucet, Arnaud, Johansen, Adam M. and Tadić, Vladislav B. (2010) On solving integral equations using Markov chain Monte Carlo methods. Applied Mathematics and Computation, Vol.216 (No.10). pp. 2869-2880. doi:10.1016/j.amc.2010.03.138 ISSN 0096-3003.
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Official URL: http://dx.doi.org/10.1016/j.amc.2010.03.138
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.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
| Library of Congress Subject Headings (LCSH): | Fredholm equations, Markov processes, Monte Carlo method | ||||
| Journal or Publication Title: | Applied Mathematics and Computation | ||||
| Publisher: | Elsevier Science Inc | ||||
| ISSN: | 0096-3003 | ||||
| Official Date: | 15 July 2010 | ||||
| Dates: |
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| Volume: | Vol.216 | ||||
| Number: | No.10 | ||||
| Number of Pages: | 12 | ||||
| Page Range: | pp. 2869-2880 | ||||
| DOI: | 10.1016/j.amc.2010.03.138 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Date of first compliant deposit: | 3 December 2015 | ||||
| Date of first compliant Open Access: | 3 December 2015 |
Data sourced from Thomson Reuters' Web of Knowledge
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