Testing the first-order separability hypothesis for spatio-temporal point patterns

Non-Parametric Analysis of Spatial and Spatio-Temporal Point Patterns

“…We split the spatial window W into 20 disjoint rectangular subsets with roughly the same area. As the separability of the intensity might be thought of as the independence of two random variables, it can be tested by a simple χ 2 -test as proposed by Ghorbani et al (2021), where the null hypothesis is separability. The test bases on the counts of points in disjoint spatial and temporal sub-regions; when there are expected counts of individual cells below 5, the authors recommend a Fisher's test.…”

“…# This takes roughly 20 seconds to be executed SepTest <-separability.test(Aegiss, nx = 5, ny = 4, nt = 16, nperm = 50000) SepTest #> #> Separability test based on Fisher's for counting data #> #> data: Point pattern Aegiss #> p-value = 0.00392 #> alternative hypothesis: The point pattern Aegiss is not spatio-temporal separable As the p-value is significant, we opt for estimating the spatio-temporal intensity in a non-separable fashion. We estimate the intensity by employing the following estimator, which uses a Gaussian kernel for all coordinates (Choi and Hall 1999;González, Hahn, and Mateu 2019;Ghorbani et al 2021)…”