PAIRWISE INTERACTION FUNCTION ESTIMATION OF STATIONARY GIBBS POINT PROCESSES USING BASIS EXPANSION

• 成果类型: Article
• 署名作者: Ba, Ismaila; Coeurjolly, Jean-Francois; Cuevas-Pacheco, Francisco
• 署名单位: University of Quebec; University of Quebec Montreal; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; Universidad Tecnica Federico Santa Maria
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2284
• 发表日期: 2023
• 页码: 1134-1158
• 关键词: maximum pseudolikelihood; bayesian-inference; Potential function; likelihood; MODEL; approximation; simulation; intensity

摘要

The class of Gibbs point processes (GPP) is a large class of spatial point processes able to model both clustered and repulsive point patterns. They are specified by their conditional intensity, which for a point pattern x and a loca-tion u, is roughly speaking the probability that an event occurs in an infinites-imal ball around u given the rest of the configuration is x. The most simple and natural class of models is the class of pairwise interaction point processes where the conditional intensity depends on the number of points and pairwise distances between them. This paper is concerned with the problem of esti-mating the pairwise interaction function nonparametrically. We propose to estimate it using an orthogonal series expansion of its logarithm. Such an ap-proach has numerous advantages compared to existing ones. The estimation procedure is simple, fast and completely data-driven. We provide asymptotic properties such as consistency and asymptotic normality and show the effi-ciency of the procedure through simulation experiments and illustrate it with several data sets.