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 corre- lation function, including shot noise Cox processes and log Gaussian Cox processes, and we develop estimation procedures using summary statis- tics and Bayesian methods. Our methodology is illustrated on real and synthetic datasets of spatial point patterns.

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.