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Particle Markov chain Monte Carlo for efficient numerical simulation. (English) Zbl 1184.65001

L’ Ecuyer, Pierre (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 2008. Proceedings of the 8th international conference Monte Carlo and quasi-Monte Carlo methods in scientific computing, Montréal, Canada, July 6–11, 2008. Berlin: Springer (ISBN 978-3-642-04106-8/hbk). 45-60 (2009).
Summary: Markov Chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods are the two most popular classes of algorithms used to sample from general high-dimensional probability distributions. The theoretical convergence of MCMC algorithms is ensured under weak assumptions, but their practical performance is notoriously unsatisfactory when the proposal distributions used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to systematically design potentially very efficient high-dimensional proposal distributions for MCMC by using SMC techniques. We demonstrate how this novel approach allows us to design effective MCMC algorithms in complex scenarios. This is illustrated by a problem of Bayesian inference for a stochastic kinetic model.
For the entire collection see [Zbl 1178.65002].

MSC:

65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
60J22 Computational methods in Markov chains
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