1st International ICST Conference on Performance Evaluation Methodologies and Tools

Research Article

On the efficiency of adaptive MCMC algorithms

Cite
BibTeX Plain Text
  • @INPROCEEDINGS{10.1145/1190095.1190150,
    author={Christophe  Andrieu and Y.F.  Atchade},
    title={On the efficiency of adaptive MCMC algorithms},
    proceedings={1st International ICST Conference on Performance Evaluation Methodologies and Tools},
    publisher={ACM},
    proceedings_a={VALUETOOLS},
    year={2012},
    month={4},
    keywords={Adaptive Markov chains Coupling Markov Chain Monte Carlo Metropolis Algorithm Stochastic Approximation Rate of convergence.},
    doi={10.1145/1190095.1190150}
}
  • Christophe Andrieu
    Y.F. Atchade
    Year: 2012
    On the efficiency of adaptive MCMC algorithms
    VALUETOOLS
    ACM
    DOI: 10.1145/1190095.1190150
Christophe Andrieu1,*, Y.F. Atchade2,*
  • 1: Mathematics Department, University of Bristol, Bristol, UK.
  • 2: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada.
*Contact email: c.andrieu@bris.ac.uk, yatchade@uottawa.ca

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 process and "optimal" (nonadaptive) MCMC algorithm share identical 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 [1]. We also propose a new class of adaptive MCMC algorithms, called quasi-perfect adaptive MCMC which possesses appealing theoretical and practical properties, as demonstrated through numerical simulations.

Keywords
Adaptive Markov chains Coupling Markov Chain Monte Carlo Metropolis Algorithm Stochastic Approximation Rate of convergence.
Published
2012-04-12
Publisher
ACM
http://dx.doi.org/10.1145/1190095.1190150
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