Stein's method for discrete Gibbs measures

Stein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. 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 exampl...

Volledige beschrijving

Bibliografische gegevens
Hoofdauteurs: Eichelsbacher, P, Reinert, G
Formaat: Journal article
Taal:English
Gepubliceerd in: 2008
_version_ 1826289826062663680
author Eichelsbacher, P
Reinert, G
author_facet Eichelsbacher, P
Reinert, G
author_sort Eichelsbacher, P
collection OXFORD
description Stein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. 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].
first_indexed 2024-03-07T02:34:49Z
format Journal article
id oxford-uuid:a870d22b-4f17-44ba-8478-2a9ab3d51e5e
institution University of Oxford
language English
last_indexed 2024-03-07T02:34:49Z
publishDate 2008
record_format dspace
spelling oxford-uuid:a870d22b-4f17-44ba-8478-2a9ab3d51e5e2022-03-27T03:01:31ZStein's method for discrete Gibbs measuresJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a870d22b-4f17-44ba-8478-2a9ab3d51e5eEnglishSymplectic Elements at Oxford2008Eichelsbacher, PReinert, GStein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. 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].
spellingShingle Eichelsbacher, P
Reinert, G
Stein's method for discrete Gibbs measures
title Stein's method for discrete Gibbs measures
title_full Stein's method for discrete Gibbs measures
title_fullStr Stein's method for discrete Gibbs measures
title_full_unstemmed Stein's method for discrete Gibbs measures
title_short Stein's method for discrete Gibbs measures
title_sort stein s method for discrete gibbs measures
work_keys_str_mv AT eichelsbacherp steinsmethodfordiscretegibbsmeasures
AT reinertg steinsmethodfordiscretegibbsmeasures