Stationarity Tests for Spatial Point Processes using Discrepancies

Stationarity tests for spatial point processes using discrepancies.

For testing stationarity of a given spatial point pattern, Guan (2008) proposed a model-free statistic, based on the deviations between observed and expected counts of points in expanding regions within the sampling window. This article extends his method to a general class of statistics by incorporating also such information when points are projected to the axes and by allowing different ways ...

A KPSS test for stationarity for spatial point processes.

We propose a formal method to test stationarity for spatial point processes. The proposed test statistic is based on the integrated squared deviations of observed counts of events from their means estimated under stationarity. We show that the resulting test statistic converges in distribution to a functional of a two-dimensional Brownian motion. To conduct the test, we compare the calculated s...

Filters for Spatial Point Processes

We study the general problem of estimating a ‘hidden’ point process X given the realisation of an ‘observed’ point process Y (possibly defined in different spaces) with known joint distribution. We characterise the posterior distribution of X under marginal Poisson and Gauss-Poisson prior and when the transformation from X to Y includes thinning, displacement and augmentation with extra points....

Spatial Point Processes

Property (iv) is called boundedly finite. So, when we use (iv) instead of (iii), we are interested in simple, boundedly finite spatial point processes with no fixed atoms. When we use (iii), the domain A can be an arbitrary set. When we use (iv), the domain A must have some notion of boundedness. This is no problem when A is a subset of Rd for some d. We just use the usual notion of boundedness...

Point processes , spatial – temporal