Volume 19, 2007Conference Oxford sur les méthodes de Monte Carlo séquentielles
|Page(s)||79 - 84|
|Published online||30 October 2007|
Non-linear Markov Chain Monte Carlo
Department of Mathematics, University of Bristol, UK
2 Department of Mathematics, Imperial College London, UK
3 Departments of Statistics & Computer Science, University of British Columbia, CA
4 Department of Mathematics, University of Nice Sophia Antipolis, FR
In this paper we introduce a class of non-linear Markov Chain Monte Carlo (MCMC) methods for simulating from a probability measure π. Non-linear Markov kernels (e.g. Del Moral (2004)) can be constructed to admit π as an invariant distribution and have typically superior mixing properties to ordinary (linear) MCMC kernels. However, such non-linear kernels often cannot be simulated exactly, so, in the spirit of particle approximations of Feynman-Kac formulae (Del Moral 2004), we construct approximations of the non-linear kernels via Self-Interacting Markov Chains (Del Moral & Miclo, Proc. R. Soc. Lond. A, 460, 325-46, 2004.) (SIMC). We present several non-linear kernels and investigate the performance of our approximations with some simulations.
© EDP Sciences, ESAIM, 2007
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