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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	975-1001
Number of pages	27
Journal	Bernoulli
Volume	18
Issue number	3
DOIs	https://doi.org/10.3150/11-BEJ360
Publication status	Published - 1 Aug 2012

Keywords

Adaptive Markov chain Monte Carlo
Markov chain
Metropolis adjusted Langevin algorithms
Stochastic approximations
Subgeometric ergodicity

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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.",

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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

Abstract

Keywords

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