Logistic regression for spatial Gibbs point processes

• 成果类型: Article
• 署名作者: Baddeley, Adrian; Coeurjolly, Jean-Francois; Rubak, Ege; Waagepetersen, Rasmus
• 署名单位: University of Western Australia; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; Aalborg University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast060
• 发表日期: 2014
• 页码: 377392
• 关键词: maximum pseudolikelihood; likelihood estimators; RESIDUALS; EXISTENCE; geometry; models

摘要

We propose a computationally efficient technique, based on logistic regression, for fitting Gibbs point process models to spatial point pattern data. The score of the logistic regression is an unbiased estimating function and is closely related to the pseudolikelihood score. Implementation of our technique does not require numerical quadrature, and thus avoids a source of bias inherent in other methods. For stationary processes, we prove that the parameter estimator is strongly consistent and asymptotically normal, and propose a variance estimator. We demonstrate the efficiency and practicability of the method on a real dataset and in a simulation study.