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Issue ESAIM: Proc.
Volume 19, 2007
Conference Oxford sur les méthodes de Monte Carlo séquentielles
Page(s) 79 - 84
DOI http://dx.doi.org/10.1051/proc:071911
Published online 30 October 2007

ESAIM: Proc., 2007, Vol. 19, pp. 79-84
DOI: 10.1051/proc:071911

Non-linear Markov Chain Monte Carlo

Christophe Andrieu1, Ajay Jasra2, Arnaud Doucet3 and Pierre Del Moral4

1  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


(Published online: 30 October 2007)

Abstract
In this paper we introduce a class of non-linear Markov Chain Monte Carlo (MCMC) methods for simulating from a probability measure $\pi$. Non-linear Markov kernels (e.g. Del Moral (2004)) can be constructed to admit $\pi$ 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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