ANALYSIS OF SPATIAL POINT PATTERNS BY KERNEL IDENTIFICATION

In the analysis of spatial point patterns, complete spatial randomness (CSR) hypothesis, which is a restriction of a homogenous Poisson process to study region A, operates as a dividing hypothesis between “regular” and “aggregated” patterns. Meanwhile, many alternatives to CSR in aggregated patterns are extensions of homogenous Poisson processes themselves. Therefore, when the CSR hypothesis is rejected, results related to Poisson processes may be used to formulate plausible alternatives to CSR. In this paper, we propose a new statistic for testing CSR and then by applying it in conjunction with a notion of kernels of a point pattern, we determine the “parents” of a Poisson cluster process when the CSR hypothesis is rejected and a Neyman-Scott process is assumed for the point pattern under alternative hypothesis. We have made power studies for our test statistic by simulation, and have also surveyed the performance of our method on a certain point pattern. Finally, the whole method is carried on certain real life data.