On the efficiency of adaptive MCMC algorithms

Christophe Andrieu; Yves F. Atchadé

On the efficiency of adaptive MCMC algorithms

Christophe Andrieu^*
, Yves F. Atchadé

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

26 Citations (Scopus)

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 et al. (2001).

Original language	English
Pages (from-to)	336-349
Number of pages	14
Journal	Electronic Communications in Probability
Volume	12
Publication status	Published - 12 Oct 2007

Keywords

Adaptive Markov chains
Coupling
Markov chain Monte Carlo
Metropolis algorithm
Rate of convergence
Stochastic approximation

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title = "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 et al. (2001).",

keywords = "Adaptive Markov chains, Coupling, Markov chain Monte Carlo, Metropolis algorithm, Rate of convergence, Stochastic approximation",

author = "Christophe Andrieu and Atchad{\'e}, \{Yves F.\}",

year = "2007",

month = oct,

day = "12",

language = "English",

volume = "12",

pages = "336--349",

journal = "Electronic Communications in Probability",

issn = "1083-589X",

publisher = "Institute of Mathematical Statistics",

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TY - JOUR

T1 - On the efficiency of adaptive MCMC algorithms

AU - Andrieu, Christophe

AU - Atchadé, Yves F.

PY - 2007/10/12

Y1 - 2007/10/12

N2 - 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 et al. (2001).

AB - 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 et al. (2001).

KW - Adaptive Markov chains

KW - Coupling

KW - Markov chain Monte Carlo

KW - Metropolis algorithm

KW - Rate of convergence

KW - Stochastic approximation

UR - https://www.scopus.com/pages/publications/35548982235

M3 - Article (Academic Journal)

AN - SCOPUS:35548982235

SN - 1083-589X

VL - 12

SP - 336

EP - 349

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -

On the efficiency of adaptive MCMC algorithms

Abstract

Keywords

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