Parametric estimation of pairwise Gibbs point processes with infinite range interaction

Parametric estimation of pairwise Gibbs point processes with infinite range interaction

Nonparametric Estimation of Interaction Functions of Pairwise Interaction Point Processes

The new problem of nonparametric estimation of the interaction function of pairwise interaction point processes is addressed. We rst generalize some limit theorems of Saunders and Funk. Then we propose a very simple nonparametric estimation method based on the generalization. Several examples are shown to illustrate its eecacy.

Poisson intensity parameter estimation for stationary Gibbs point processes of finite interaction range

We introduce a semi-parametric estimator of the Poisson intensity parameter of a spatial stationary Gibbs point process. Under very mild assumptions satisfied by a large class of Gibbs models, we establish its strong consistency and asymptotic normality. We also consider its finite-sample properties in a simulation study.

Nonparametric estimation of interaction functions for two-type pairwise interaction point processes

Nonparametric estimation of interaction functions for twotype pairwise interaction point processes is addressed. Such a problem is known to be challenging due to the intractable normalizing constant present in the density function. It is shown that the means of the marked interpoint distance functions embedded in the two-type pairwise interaction point process converge to the means of an inhomo...

Perfect simulation of infinite range Gibbs measures and coupling with their finite range approximations

In this paper we address the questions of perfectly sampling a Gibbs measure with infinite range interactions and of perfectly sampling the measure together with its finite range approximations. We solve these questions by introducing a perfect simulation algorithm for the measure and for the coupled measures. The algorithm works for general Gibbsian interaction under requirements on the tails ...