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To appear Annals of Applied Probability 2005Vol. 0, No. 0, 18
 

Summary: To appear Annals of Applied Probability
2005Vol. 0, No. 0, 1­8
ON THE ERGODICITY PROPERTIES OF SOME ADAPTIVE MCMC
ALGORITHMS
By Christophe Andrieu, and ´Eric Moulines
University of Bristol and ´Ecole Nationale Sup´erieure des T´el´ecommunications
In this paper we study the ergodicity properties of some adap-
tive Monte Carlo Markov chain algorithms (MCMC) that have been
recently proposed in the literature. We prove that under a set of ver-
ifiable conditions, ergodic averages calculated from the output of a
so-called adaptive MCMC sampler converge to the required value and
can even, under more stringent assumptions, satisfy a central limit
theorem. We prove that the conditions required are satisfied for the
Independent Metropolis-Hastings algorithm and the Random Walk
Metropolis algorithm with symmetric increments. Finally we propose
an application of these results to the case where the proposal distrib-
ution of the Metropolis-Hastings update is a mixture of distributions
from a curved exponential family.
1. Introduction. Markov chain Monte Carlo (MCMC), introduced by Metropolis
et al. (1953), is a popular computational method for generating samples from virtually any

  

Source: Andrieu, Christophe- Department of Mathematics, University of Bristol

 

Collections: Mathematics