Electronic Communications in Probability

On the efficiency of adaptive MCMC algorithms

Christophe Andrieu and Yves Atchade

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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].

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Electron. Commun. Probab., Volume 12 (2007), paper no. 33, 336-349.

Accepted: 12 October 2007
First available in Project Euclid: 6 June 2016

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Andrieu, Christophe; Atchade, Yves. On the efficiency of adaptive MCMC algorithms. Electron. Commun. Probab. 12 (2007), paper no. 33, 336--349. doi:10.1214/ECP.v12-1320. https://projecteuclid.org/euclid.ecp/1465224976

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