期刊
ANNALS OF APPLIED PROBABILITY
卷 18, 期 3, 页码 1201-1214出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/07-AAP486
关键词
Markov chain Monte Carlo; Metropolis-Hastings algorithm; central limit theorem; variance; Peskun order; geometric ergodicity; spectrum
资金
- Engineering and Physical Sciences Research Council [EP/D002060/1] Funding Source: researchfish
We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L-2 functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Peskun order. We close with some applications to Metropolis-Hastings algorithms.
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