On solving integral equations using Markov chain Monte Carlo methods |
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Authors: | Arnaud Doucet Vladislav B Tadi? |
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Institution: | a Departments of Statistics and Computer Science, University of British Columbia, Vancouver, BC, Canada b Department of Mathematics, University of Bristol, Bristol, UK |
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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. |
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Keywords: | Fredholm equation Trans-dimensional Markov chain Monte Carlo Sequential Importance Sampling Sequential Monte Carlo |
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