Conference Agenda

In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations around the origin. Most statistical tests for the null hypothesis of isotropy found in the literature are based either on asymptotics or on Monte Carlo simulation of a parametric null model. However, fitting a parametric null model is challenging in case of anisotropy and asymptotic distributions are only available to a limited extent.

In this talk, we present a novel nonparametric and computationally cheap test for the hypothesis of isotropy for stationary point processes. Our test is based on resampling the Fry points which are the pairwise difference vectors of the observed point pattern. The resampling itself is achieved by using random rotation techniques. We investigate empirical levels and powers of the proposed test in a simulation study for a diverse set of point process models. Anisotropic point process models are hereby obtained either via the geometric anisotropy mechanism or through oriented clusters where the orientation distribution is given by a von-Mises-Fisher distribution. Finally, a real data set of amacrine cells is tested for isotropy.