Results 1  10
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46
FixedWidth Output Analysis for Markov Chain Monte Carlo
, 2005
"... Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a target distribution via ergodic averages. A fundamental question is when should sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a metho ..."
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Cited by 93 (30 self)
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Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a target distribution via ergodic averages. A fundamental question is when should sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a userspecified value. Hence calculating a Monte Carlo standard error is a critical step in assessing the simulation output. We consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We give sufficient conditions for the strong consistency of both methods and investigate their finite sample properties in a variety of examples.
On the Markov chain central limit theorem. Probability Surveys
, 2004
"... The goal of this mainly expository paper is to describe conditions which guarantee a central limit theorem for functionals of general state space Markov chains with a view towards Markov chain Monte Carlo settings. Thus the focus is on the connections between drift and mixing conditions and their im ..."
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Cited by 82 (14 self)
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The goal of this mainly expository paper is to describe conditions which guarantee a central limit theorem for functionals of general state space Markov chains with a view towards Markov chain Monte Carlo settings. Thus the focus is on the connections between drift and mixing conditions and their implications. In particular, we consider three commonly cited central limit theorems and discuss their relationship to classical results for mixing processes. Several motivating examples are given which range from toy onedimensional settings to complicated settings encountered in Markov chain Monte Carlo. 1
Limit theorems for some adaptive MCMC algorithms with subgeometric kernels. Part II
, 2009
"... We prove a central limit theorem for a general class of adaptive Markov Chain Monte Carlo algorithms driven by subgeometrically 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 ..."
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Cited by 28 (4 self)
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We prove a central limit theorem for a general class of adaptive Markov Chain Monte Carlo algorithms driven by subgeometrically 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.
Convergence properties of pseudomarginal Markov Chain Monte Carlo algorithms. Annals of Applied Probability
, 2012
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Subgeometric ergodicity of strong Markov processes
 ANN.APPL.PROBAB
, 2005
"... We derive sufficient conditions for subgeometric fergodicity of strongly Markovian processes. We first propose a criterion based on modulated moment of some delayed returntime to a petite set. We then formulate a criterion for polynomial fergodicity in terms of a drift condition on the generator. ..."
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Cited by 15 (1 self)
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We derive sufficient conditions for subgeometric fergodicity of strongly Markovian processes. We first propose a criterion based on modulated moment of some delayed returntime to a petite set. We then formulate a criterion for polynomial fergodicity in terms of a drift condition on the generator. Applications to specific processes are considered, including Langevin tempered diffusions on R n and storage models.
BOUNDS ON REGENERATION TIMES AND LIMIT THEOREMS FOR SUBGEOMETRIC MARKOV CHAINS
, 2006
"... This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded functional of the Markov chains under drift and minorization co ..."
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Cited by 13 (0 self)
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This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded functional of the Markov chains under drift and minorization conditions which are weaker than the FosterLyapunov conditions. The regenerationsplit chain method and a precise control of the modulated moment of the hitting time to small sets are employed in the proof.
Statedependent FosterLyapunov criteria for subgeometric convergence of Markov chains
 Stoch. Process Appl
, 2009
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Computable convergence rates for subgeometric ergodic Markov chains
 Bernoulli
, 2007
"... Abstract. In this paper, we give quantitative bounds on the ftotal variation distance from convergence of an Harris recurrent Markov chain on an arbitrary under drift and minorisation conditions implying ergodicity at a subgeometric rate. These bounds are then specialized to the stochastically mon ..."
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Cited by 11 (1 self)
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Abstract. In this paper, we give quantitative bounds on the ftotal variation distance from convergence of an Harris recurrent Markov chain on an arbitrary under drift and minorisation conditions implying ergodicity at a subgeometric rate. These bounds are then specialized to the stochastically monotone case, covering the case where there is no minimal reachable element. The results are illustrated on two examples from queueing theory and Markov Chain Monte Carlo.