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 Electronic Communications in Probability > Vol. 12 (2007) > Paper 33 open journal systems 


On the efficiency of adaptive MCMC algorithms

Christophe Andrieu, University of Bristol
Yves Atchade, University of Michigan


Abstract
We study a class of adaptive Markov Chain Monte Carlo (MCMC) processes which aim at behaving as an ``optimal'' target process via a learning procedure. We show, under appropriate conditions, that the adaptive MCMC chain and the ``optimal'' (nonadaptive) MCMC process share many asymptotic properties. The special case of adaptive MCMC algorithms governed by stochastic approximation is considered in details and we apply our results to the adaptive Metropolis algorithm of [Haario, Saksman, Tamminen].


Full text: PDF

Pages: 336-349

Published on: October 12, 2007


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Electronic Communications in Probability. ISSN: 1083-589X