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...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2008
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| _version_ | 1826289826062663680 |
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| 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 |