 On the rate of convergence of the Gibbs sampler for the 1-D Ising model by geometric boundShang-Ying Shiu and Ting-Li Chen Statistics & Probability Letters, 2015, vol. 105, issue C, 14-19 Abstract: The second largest eigenvalue in absolute value determines the rate of convergence of the Markov chain Monte Carlo methods. In this paper we consider the Gibbs sampler for the 1-D Ising model. We apply the geometric bound by Diaconis and Stroock (1991) to calculate an upper bound of the second largest eigenvalue, which we show is also a bound of the second largest eigenvalue in absolute value. Based on this upper bound, we derive that the convergence time is O(n2), where n is the number of sites. Our result includes a constant of proportionality, which enables us to give a precise bound of the convergence time. The results presented in this paper provide the lowest bound compared to those with a constant of proportionality in the literature. Keywords: Markov chain Monte Carlo; Rate of convergence; Gibbs sampler; Ising model (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:105:y:2015:i:c:p:14-19 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2015.06.004 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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