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September 2014 Gibbs point process approximation: Total variation bounds using Stein’s method
Dominic Schuhmacher, Kaspar Stucki
Ann. Probab. 42(5): 1911-1951 (September 2014). DOI: 10.1214/13-AOP895


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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Dominic Schuhmacher. Kaspar Stucki. "Gibbs point process approximation: Total variation bounds using Stein’s method." Ann. Probab. 42 (5) 1911 - 1951, September 2014.


Published: September 2014
First available in Project Euclid: 29 August 2014

zbMATH: 1322.60060
MathSciNet: MR3262495
Digital Object Identifier: 10.1214/13-AOP895

Primary: 60G55
Secondary: 60J75 , 82B21

Keywords: Birth–death process , Conditional intensity , pairwise interaction process , Stein’s method , total variation distance

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 5 • September 2014
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