Tests for isotropy in spatial point patterns – A comparison of statistical indices

Authors

Affiliations

Tuomas Rajala

Natural Resources Institute Finland

Claudia Redenbach

Technische Universität Kaiserslautern

Aila Särkkä

Chalmers University of Technology and the University of Gothenburg

Martina Sormani

Technische Universität Kaiserslautern & Fraunhofer Institut für Techno- und Wirtschaftsmathematik

Code: All of the summary statistics are implemented in Kdirectional

I wrote a short summary here.

Abstract

Isotropy of a point process, defined as invariance of the distribution under rotation, is often assumed in spatial statistics. Formal tests for the hypothesis of isotropy can be created by comparing directional summary statistics in different directions. In this paper, the statistical powers of tests based on a variety of summary statistics and several choices of deviance measures are compared in a simulation study. Four models for anisotropic point processes are considered covering both regular and clustered cases. We discuss the robustness of the results to changes of the tuning parameters, and highlight the strengths and limitations of the methods.

Figure 12: Overall results of the simulation trials. For each anisotropy summary, the gray points, with shape by model, give the best power over tuning parameters, integration limits, and tests. The large dot is the mean over all powers.