Testing Stationarity, Isotropy and Equal Distribution for Spatial Point Patterns

Abstract

Data in form of point patterns are often encountered in spatial statistics, e.g. locations of a certain species of plants and locations of mines.? Point pattern analysis is often carried out by assuming the given pattern as a realisation of some spatial point process model, such as the Poisson process or the Gibbs process, and then applying parametric methods for model fitting and testing.? However, certain crucial questions that should be addressed before modeling are general and are model-free, such as whether the distribution of the model from which the data are generated is translationally invariant (stationary) and rotationally invariant (isotropic) or whether two given patterns (sampling from e.g. a normal tissue and a cancerous tissue) have the same distribution.? In this talk we review the existing tests for these questions, discuss their weaknesses, and propose new model-free testing procedures that do not suffer from such weaknesses.? Simulation results and case studies will be shown to demonstrate the advantages of our proposed tests over the tests in the literature.