LJKProbability & Statistics Seminar

On Tuesday November 23 2010 at 11h00 in Salle 1  Tour IRMA

Seminary of

Transforming spatial point processes into Poisson processes using random superpositioning

Summary

Most finite spatial point process models specified by a density are locally stable, implying that the Papangelou intensity is bounded by some integrable
function beta defined on the space for the points of the process. We show how to superpose such a locally stable spatial point process X with a
complementary spatial point process Y to obtain a Poisson process X U Y with intensity function beta, and introduce a fast and easy simulation
procedure for Y conditional on X. This may be used for model checking: given a model for the Papangelou intensity of the original spatial point process, this model is used to generate the complementary process, and the resulting superposition is a Poisson process with intensity function beta if and only if the true
Papangelou intensity is used. Whether the superposition is actually such a Poisson process can easily be examined using well known results and fast simulation procedures for Poisson processes. We illustrate this approach to
model checking in the case of a Strauss process.
