Journal Article

Logistic regression for spatial Gibbs point processes

Adrian Baddeley, Jean-François Coeurjolly, Ege Rubak and Rasmus Waagepetersen

in Biometrika

Published on behalf of The Biometrika Trust

Volume 101, issue 2, pages 377-392
Published in print June 2014 | ISSN: 0006-3444
Published online March 2014 | e-ISSN: 1464-3510 | DOI: https://dx.doi.org/10.1093/biomet/ast060
Logistic regression for spatial Gibbs point processes

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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.

Keywords: Estimating function; Exponential family model; Georgii–Nguyen–Zessin formula; Logistic regression; Pseudolikelihood

Journal Article.  0 words. 

Subjects: Biomathematics and Statistics ; Probability and Statistics

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