Limit theorems for some adaptive MCMC algorithms with subgeometric kernels
Yves Atchadé and Gersende Fort
Source: Bernoulli Volume 16, Number 1
(2010), 116-154.
Abstract
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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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bj/1265984706
Digital Object Identifier: doi:10.3150/09-BEJ199
Mathematical Reviews number (MathSciNet): MR2648752
Zentralblatt MATH identifier: 1215.60046
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