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Geometric Anisotropic Spatial Point Pattern Analysis and Cox Processes
Author(s) -
Møller Jesper,
Toftaker Håkon
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12041
Subject(s) - point process , mathematics , cox process , anisotropy , gaussian process , statistical physics , correlation function (quantum field theory) , gaussian , function (biology) , spatial correlation , bayesian probability , statistics , poisson distribution , physics , poisson process , spectral density , quantum mechanics , evolutionary biology , biology
We consider spatial point processes with a pair correlation function, which depends only on the lag vector between a pair of points. Our interest is in statistical models with a special kind of ‘structured’ anisotropy: the pair correlation function is geometric anisotropic if it is elliptical but not spherical. In particular, we study Cox process models with an elliptical pair correlation function, including shot noise Cox processes and log Gaussian Cox processes, and we develop estimation procedures using summary statistics and Bayesian methods. Our methodology is illustrated on real and synthetic datasets of spatial point patterns.