We consider spatial point processes with a pair correlation function g(u) which depends only on the lag vector u between a pair of points. Our interest is in statistical models with a special kind of ‘structured’ anisotropy: g is geometric anisotropy 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.