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

Dominic Schuhmacher; Kaspar Stucki

doi:10.1214/13-aop895

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arXiv · 1207.3096

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

Dominic Schuhmacher·Kaspar Stucki

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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.

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BibTeX RIS

Dominic Schuhmacher, Kaspar Stucki. 2014-09-12. Gibbs point process approximation: Total variation bounds using Stein's method. https://doi.org/10.1214/13-aop895

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