Journal article
Stein's method for discrete Gibbs measures
- Abstract:
- 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].
- Publication status:
- Published
Actions
Authors
- Journal:
- Annals of Applied Probability More from this journal
- Volume:
- 18
- Issue:
- 4
- Pages:
- 1588-1618
- Publication date:
- 2008-08-21
- DOI:
- EISSN:
-
1050-5164
- ISSN:
-
1050-5164
- Language:
-
English
- Keywords:
- Pubs id:
-
pubs:97526
- UUID:
-
uuid:a870d22b-4f17-44ba-8478-2a9ab3d51e5e
- Local pid:
-
pubs:97526
- Source identifiers:
-
97526
- Deposit date:
-
2012-12-19
Terms of use
- Copyright date:
- 2008
- Notes:
-
Published 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)
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