Convergence of adaptive and interacting Markov chain Monte Carlo algorithms

2012/03/14 by G. Fort, E. Moulines, P. Priouret · 1 citation
Mathematics · #math.ST #stat.TH

paper · pdf · doi:10.1214/11-aos938

published as Annals of Statistics 2011, Vol. 39, No. 6, 3262-3289 · Published in at http://dx.doi.org/10.1214/11-AOS938 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

arxiv created 2012/03/14 · arxiv updated 2012/03/15

Abstract

Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions. Motivated by some recently introduced algorithms (such as the adaptive Metropolis algorithm and the interacting tempering algorithm), we develop a general methodological and theoretical framework to establish both the convergence of the marginal distribution and a strong law of large numbers. This framework weakens the conditions introduced in the pioneering paper by Roberts and Rosenthal [J. Appl. Probab. 44 (2007) 458--475]. It also covers the case when the target distribution π is sampled by using Markov transition kernels with a stationary distribution that differs from π.

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