Dominic Schuhmacher
Georg-August Universitaet Goettingen
Stein's method for Gibbs process approximation
In this talk we consider Gibbs point processes on a compact metric space. We will
derive upper bounds for the total variation distance between a general Gibbs process
distribution and one that satisfies a certain stability condition.
Stein's method was first presented in 1972 for normal approximation and is nowadays
a well-established set of recipes for deriving upper bounds between probability
distributions in a wide range of situations. The outline of the general technique is
given, and we then present the particular elaboration needed to obtain our upper
bounds in the Gibbs process setting. For this we will construct a coupling between
two identical spatial-birth death processes started at different configurations.
Several examples for the upper bounds obtained are also presented.