Gibbs point process approximation: Total variation bounds using Stein’s method
2014 | journal article. A publication with affiliation to the University of Göttingen.
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- Authors
- Schuhmacher, Dominic; Stucki, Kaspar
- Abstract
- 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.
- Issue Date
- 2014
- Status
- published
- Publisher
- Institute of Mathematical Statistics
- Journal
- The Annals of Probability
- ISSN
- 0091-1798
- Sponsor
- Swiss National Science Foundation [200021-137527]