We present a new class of interacting Markov chain Monte Carlo algorithms 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 evolutions depend on the occupation measure of their 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 behavior of these iterative algorithms which relies on measure-valued processes and semigroup techniques. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman–Kac distribution flows.
Publié le : 2010-04-15
Classification:
Markov chain Monte Carlo methods,
sequential Monte Carlo methods,
self-interacting processes,
time-inhomogeneous Markov chains,
Metropolis–Hastings algorithm,
Feynman–Kac formulae,
47H20,
60G35,
60J85,
62G09,
47D08,
47G10,
62L20
@article{1268143434,
author = {Del Moral, Pierre and Doucet, Arnaud},
title = {Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations},
journal = {Ann. Appl. Probab.},
volume = {20},
number = {1},
year = {2010},
pages = { 593-639},
language = {en},
url = {http://dml.mathdoc.fr/item/1268143434}
}
Del Moral, Pierre; Doucet, Arnaud. Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations. Ann. Appl. Probab., Tome 20 (2010) no. 1, pp. 593-639. http://gdmltest.u-ga.fr/item/1268143434/