1Department of Mathematics, University of Bristol, UK 2Department of Mathematics, Imperial College London, UK 3Departments of Statistics & Computer Science, University of British Columbia, CA 4Department of Mathematics, University of Nice Sophia Antipolis, FR
ESAIM. Proceedings, Tome 19 (2007), pp. 79-84
Cet article a éte moissonné depuis la source EDP Sciences
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.
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
@article{EP_2007_19_a11,
author = {Christophe Andrieu and Ajay Jasra and Arnaud Doucet and Pierre Del Moral},
title = {Non-linear {Markov} {Chain} {Monte} {Carlo}},
journal = {ESAIM. Proceedings},
pages = {79--84},
year = {2007},
volume = {19},
doi = {10.1051/proc:071911},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:071911/}
}
TY - JOUR
AU - Christophe Andrieu
AU - Ajay Jasra
AU - Arnaud Doucet
AU - Pierre Del Moral
TI - Non-linear Markov Chain Monte Carlo
JO - ESAIM. Proceedings
PY - 2007
SP - 79
EP - 84
VL - 19
UR - http://geodesic.mathdoc.fr/articles/10.1051/proc:071911/
DO - 10.1051/proc:071911
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%A Ajay Jasra
%A Arnaud Doucet
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%J ESAIM. Proceedings
%D 2007
%P 79-84
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%U http://geodesic.mathdoc.fr/articles/10.1051/proc:071911/
%R 10.1051/proc:071911
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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
