Bernoulli

  • Bernoulli
  • Volume 16, Number 1 (2010), 116-154.

Limit theorems for some adaptive MCMC algorithms with subgeometric kernels

Yves Atchadé and Gersende Fort

Full-text: Open access

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.

Article information

Source
Bernoulli, Volume 16, Number 1 (2010), 116-154.

Dates
First available in Project Euclid: 12 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1265984706

Digital Object Identifier
doi:10.3150/09-BEJ199

Mathematical Reviews number (MathSciNet)
MR2648752

Zentralblatt MATH identifier
1215.60046

Keywords
adaptive Markov chain Monte Carlo Markov chain subgeometric ergodicity

Citation

Atchadé, Yves; Fort, Gersende. Limit theorems for some adaptive MCMC algorithms with subgeometric kernels. Bernoulli 16 (2010), no. 1, 116--154. doi:10.3150/09-BEJ199. https://projecteuclid.org/euclid.bj/1265984706


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