Roberts, Gareth O. and Rosenthal, Jeffrey S. (2004) General state space Markov chains and MCMC algorithms. Probability Surveys, 1. pp. 20-71. ISSN 1549-5787Full text not available from this repository.
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.
|Journal or Publication Title:||Probability Surveys|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Lancaster Environment Centre|
|Deposited By:||Mrs Yaling Zhang|
|Deposited On:||13 Jun 2008 11:15|
|Last Modified:||24 Jun 2016 01:31|
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