Geodesic
Non-linear Markov Chain Monte Carlo
Christophe Andrieu1 ; Ajay Jasra2 ; Arnaud Doucet3 ; 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
ESAIM. Proceedings, Tome 19 (2007), pp. 79-84.

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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.
DOI : 10.1051/proc:071911

Christophe Andrieu 1 ; Ajay Jasra 2 ; Arnaud Doucet 3 ; Pierre Del Moral 4

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 
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     title = {Non-linear {Markov} {Chain} {Monte} {Carlo}},
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Christophe Andrieu; Ajay Jasra; Arnaud Doucet; Pierre Del Moral. Non-linear Markov Chain Monte Carlo. ESAIM. Proceedings, Tome 19 (2007), pp. 79-84. doi : 10.1051/proc:071911. http://geodesic.mathdoc.fr/articles/10.1051/proc:071911/

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