INTERACTING MARKOV CHAIN MONTE CARLO METHODS FOR SOLVING NONLINEAR MEASURE-VALUED EQUATIONS
成果类型：
Article
署名作者：
Del Moral, Pierre; Doucet, Arnaud
署名单位：
Universite de Bordeaux; University of British Columbia; University of British Columbia; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); Inria
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/09-AAP628
发表日期：
2010
页码：
593-639
关键词：
摘要：
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.