Limit theorems for some adaptive MCMC algorithms with subgeometric kernels: Part II

Yves F. Atchadé; Gersende Fort

doi:10.3150/11-BEJ360

Limit theorems for some adaptive MCMC algorithms with subgeometric kernels: Part II

Yves F. Atchadé
, Gersende Fort

École Polytechnique

University of Michigan, Ann Arbor

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We prove a central limit theorem for a general class of adaptive Markov Chain Monte Carlo algorithms driven by sub-geometrically ergodic Markov kernels. We discuss in detail the special case of stochastic approximation.We use the result to analyze the asymptotic behavior of an adaptive version of the Metropolis Adjusted Langevin algorithm with a heavy tailed target density.

langue originale	Anglais
Pages (de - à)	975-1001
Nombre de pages	27
journal	Bernoulli
Volume	18
Numéro de publication	3
Les DOIs	https://doi.org/10.3150/11-BEJ360
état	Publié - 1 août 2012

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title = "Limit theorems for some adaptive MCMC algorithms with subgeometric kernels: Part II",

abstract = "We prove a central limit theorem for a general class of adaptive Markov Chain Monte Carlo algorithms driven by sub-geometrically ergodic Markov kernels. We discuss in detail the special case of stochastic approximation.We use the result to analyze the asymptotic behavior of an adaptive version of the Metropolis Adjusted Langevin algorithm with a heavy tailed target density.",

keywords = "Adaptive Markov chain Monte Carlo, Markov chain, Metropolis adjusted Langevin algorithms, Stochastic approximations, Subgeometric ergodicity",

author = "Atchad{\'e}, \{Yves F.\} and Gersende Fort",

year = "2012",

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T1 - Limit theorems for some adaptive MCMC algorithms with subgeometric kernels

T2 - Part II

AU - Atchadé, Yves F.

AU - Fort, Gersende

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N2 - We prove a central limit theorem for a general class of adaptive Markov Chain Monte Carlo algorithms driven by sub-geometrically ergodic Markov kernels. We discuss in detail the special case of stochastic approximation.We use the result to analyze the asymptotic behavior of an adaptive version of the Metropolis Adjusted Langevin algorithm with a heavy tailed target density.

AB - We prove a central limit theorem for a general class of adaptive Markov Chain Monte Carlo algorithms driven by sub-geometrically ergodic Markov kernels. We discuss in detail the special case of stochastic approximation.We use the result to analyze the asymptotic behavior of an adaptive version of the Metropolis Adjusted Langevin algorithm with a heavy tailed target density.

KW - Adaptive Markov chain Monte Carlo

KW - Markov chain

KW - Metropolis adjusted Langevin algorithms

KW - Stochastic approximations

KW - Subgeometric ergodicity

U2 - 10.3150/11-BEJ360

DO - 10.3150/11-BEJ360

M3 - Article

AN - SCOPUS:84873393871

SN - 1350-7265

VL - 18

SP - 975

EP - 1001

JO - Bernoulli

JF - Bernoulli

IS - 3

ER -

Limit theorems for some adaptive MCMC algorithms with subgeometric kernels: Part II

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