DEL MORAL, Pierre; DOUCET, Arnaud

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DEL MORAL, Pierre
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]

DOUCET, Arnaud
Department of Statistics [Vancouver] [UBC Statistics]
Dept of Statistics & Dept of Computer Science

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Article de revue

Ce document a été publié dans

The Annals of Applied Probability. 2010, vol. 20, n° 2, p. 593-639

Institute of Mathematical Statistics (IMS)

Résumé en anglais

We present a new interacting Markov chain Monte Carlo methodology for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution may depend on the occupation measure of the past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these algorithms as the time parameter tends to infinity. This analysis relies on measure-valued processes and semigroup techniques. We present a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions, yielding what seems to be the first results of this kind for this class of self-interacting models. We also illustrate these models in the context of Feynman-Kac distribution flows.< Réduire

Mots clés en anglais

Markov chain Monte Carlo methods

sequential Monte Carlo

self-interacting processes

time-inhomogeneous Markov chains

Metropolis-Hastings algorithm

Feynman-Kac formulae

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251