Open Access
February 2010 Limit theorems for some adaptive MCMC algorithms with subgeometric kernels
Yves Atchadé, Gersende Fort
Bernoulli 16(1): 116-154 (February 2010). DOI: 10.3150/09-BEJ199


This paper deals with the ergodicity (convergence of the marginals) and the law of large numbers for adaptive MCMC algorithms built from transition kernels that are not necessarily geometrically ergodic. We develop a number of results that significantly broaden the class of adaptive MCMC algorithms for which rigorous analysis is now possible. As an example, we give a detailed analysis of the adaptive Metropolis algorithm of Haario et al. [Bernoulli 7 (2001) 223–242] when the target distribution is subexponential in the tails.


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Yves Atchadé. Gersende Fort. "Limit theorems for some adaptive MCMC algorithms with subgeometric kernels." Bernoulli 16 (1) 116 - 154, February 2010.


Published: February 2010
First available in Project Euclid: 12 February 2010

zbMATH: 1215.60046
MathSciNet: MR2648752
Digital Object Identifier: 10.3150/09-BEJ199

Keywords: Adaptive Markov chain Monte Carlo , Markov chain , Subgeometric ergodicity

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

Vol.16 • No. 1 • February 2010
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