Gibbs point process approximation: Total variation bounds using Stein's method

Schuhmacher, Dominic; Stucki, Kaspar (2014). Gibbs point process approximation: Total variation bounds using Stein's method. The annals of probality, 42(5), pp. 1911-1951. Institute of Mathematical Statistics 10.1214/13-AOP895

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We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and statistical physics, including the comparison of two Lennard-Jones processes, hard core approximation of an area interaction process and the approximation of lattice processes by a continuous Gibbs process. Our proof of the main results is based on Stein's method. We construct an explicit coupling between two spatial birth-death processes to obtain Stein factors, and employ the Georgii-Nguyen-Zessin equation for the total bound.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Schuhmacher, Dominic and Stucki, Kaspar

Subjects:

300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics

ISSN:

0091-1798

Publisher:

Institute of Mathematical Statistics

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

07 Oct 2014 16:07

Last Modified:

25 Apr 2017 17:34

Publisher DOI:

10.1214/13-AOP895

BORIS DOI:

10.7892/boris.58617

URI:

https://boris.unibe.ch/id/eprint/58617

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