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) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |
UniBE Contributor: |
Schuhmacher, Dominic, 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: |
05 Dec 2022 14:37 |
Publisher DOI: |
10.1214/13-AOP895 |
BORIS DOI: |
10.7892/boris.58617 |
URI: |
https://boris.unibe.ch/id/eprint/58617 |
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