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Møller, Jesper; Toftaker, Håkon

Geometric anisotropic spatial point pattern analysis and Cox processes. (English) Zbl 1416.62547

Scand. J. Stat. 41, No. 2, 414-435 (2014).
Summary: 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.

Cited in 4 Documents

MSC:

62M30 Inference from spatial processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)

Keywords:

Bayesian inference; K-function; log Gaussian Cox process; minimum contrast estimation; pair correlation function; second-order intensity-reweighted stationarity; shot noise Cox process; spectral density; Whittle-Matern covariance function
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References:

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