## Electronic Communications in Probability

### On the efficiency of adaptive MCMC algorithms

#### 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].

#### Article information

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

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

https://projecteuclid.org/euclid.ecp/1465224976

Digital Object Identifier
doi:10.1214/ECP.v12-1320

Mathematical Reviews number (MathSciNet)
MR2350572

Zentralblatt MATH identifier
1129.65006

Rights

#### Citation

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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