Stein's method for discrete Gibbs measures

Simple item page
dc.creatorEichelsbacher, Peter
dc.creatorReinert, Gesine
dc.date2008-08-21
dc.date.accessioned2026-07-07T09:57:40Z
dc.date.available2026-07-07T09:57:40Z
dc.descriptionStein's method provides a way of bounding the distance of a probability distribution to a target distribution $μ$. Here we develop Stein's method for the class of discrete Gibbs measures with a density $e^V$, where $V$ is the energy function. Using size bias couplings, we treat an example of Gibbs convergence for strongly correlated random variables due to Chayes and Klein [Helv. Phys. Acta 67 (1994) 30--42]. We obtain estimates of the approximation to a grand-canonical Gibbs ensemble. As side results, we slightly improve on the Barbour, Holst and Janson [Poisson Approximation (1992)] bounds for Poisson approximation to the sum of independent indicators, and in the case of the geometric distribution we derive better nonuniform Stein bounds than Brown and Xia [Ann. Probab. 29 (2001) 1373--1403].
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AAP0498 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0808.2877
dc.identifierhttp://arxiv.org/abs/0808.2877
dc.identifierAnnals of Applied Probability 2008, Vol. 18, No. 4, 1588-1618
dc.identifierdoi:10.1214/07-AAP0498
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167428
dc.subjectProbability
dc.subject60E05 (Primary); 60F05, 60E15, 82B05 (Secondary)
dc.titleStein's method for discrete Gibbs measures
dc.typetext

Files

Collections

arXiv