General state space Markov chains and MCMC algorithms.

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General state space Markov chains and MCMC algorithms. / Roberts, Gareth O.; Rosenthal, Jeffrey S.
In: Probability Surveys, Vol. 1, 2004, p. 20-71.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Roberts, GO & Rosenthal, JS 2004, 'General state space Markov chains and MCMC algorithms.', Probability Surveys, vol. 1, pp. 20-71. <http://www.i-journals.org/ps/viewarticle.php?id=15&layout=abstract>

APA

Roberts, G. O., & Rosenthal, J. S. (2004). General state space Markov chains and MCMC algorithms. Probability Surveys, 1, 20-71. http://www.i-journals.org/ps/viewarticle.php?id=15&layout=abstract

Vancouver

Roberts GO, Rosenthal JS. General state space Markov chains and MCMC algorithms. Probability Surveys. 2004;1:20-71.

Author

Roberts, Gareth O. ; Rosenthal, Jeffrey S. / General state space Markov chains and MCMC algorithms. In: Probability Surveys. 2004 ; Vol. 1. pp. 20-71.

Bibtex

@article{dfed83a036ab4b749a03ead9acd365ae,

title = "General state space Markov chains and MCMC algorithms.",

abstract = "This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform ergodicity are presented, along with quantitative bounds on the rate of convergence to stationarity. Many of these results are proved using direct coupling constructions based on minorisation and drift conditions. Necessary and sufficient conditions for Central Limit Theorems (CLTs) are also presented, in some cases proved via the Poisson Equation or direct regeneration constructions. Finally, optimal scaling and weak convergence results for Metropolis-Hastings algorithms are discussed. None of the results presented is new, though many of the proofs are. We also describe some Open Problems.",

author = "Roberts, {Gareth O.} and Rosenthal, {Jeffrey S.}",

year = "2004",

language = "English",

volume = "1",

pages = "20--71",

journal = "Probability Surveys",

issn = "1549-5787",

publisher = "Institute of Mathematical Statistics",

}

RIS

TY - JOUR

T1 - General state space Markov chains and MCMC algorithms.

AU - Roberts, Gareth O.

AU - Rosenthal, Jeffrey S.

PY - 2004

Y1 - 2004

N2 - This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform ergodicity are presented, along with quantitative bounds on the rate of convergence to stationarity. Many of these results are proved using direct coupling constructions based on minorisation and drift conditions. Necessary and sufficient conditions for Central Limit Theorems (CLTs) are also presented, in some cases proved via the Poisson Equation or direct regeneration constructions. Finally, optimal scaling and weak convergence results for Metropolis-Hastings algorithms are discussed. None of the results presented is new, though many of the proofs are. We also describe some Open Problems.

AB - This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform ergodicity are presented, along with quantitative bounds on the rate of convergence to stationarity. Many of these results are proved using direct coupling constructions based on minorisation and drift conditions. Necessary and sufficient conditions for Central Limit Theorems (CLTs) are also presented, in some cases proved via the Poisson Equation or direct regeneration constructions. Finally, optimal scaling and weak convergence results for Metropolis-Hastings algorithms are discussed. None of the results presented is new, though many of the proofs are. We also describe some Open Problems.

M3 - Journal article

VL - 1

SP - 20

EP - 71

JO - Probability Surveys

JF - Probability Surveys

SN - 1549-5787

ER -

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