Stein's method for Gibbs point processes

Kaspar Stucki
Date and time
Conference - Stochastic Geometry

Gibbs point processes are widely used both in spatial statistics and in statistical mechanics, as they allow a very exible modelling of interaction between the points. However, a notorious difficulty with Gibbs processes is that in most cases of interest their densities can only be specied up to normalizing constants, which typically renders explicit calculations, e.g. of the total variation distance between two such processes, difficult. In this talk we develop a variant of Stein's method to compare two Gibbs processes. 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 or hard core approximation of an area interaction process. As a bi-product we also obtain bounds on the probability generating functional of a locally stable Gibbs process, which for instance yield nice estimates of the intensity of a Strauss process.


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