Multiresolution analysis of linearly oriented spatial point patterns

The assumption of direction invariance, i.e. isotropy, is often made in the practical analysis of spatial point patterns due to simpler interpretation and ease of analysis. However, this assumption is many times hard to find in real applications. We propose a wavelet-based approach to test for isotropy in spatial patterns based on the logarithm of the directional scalogram. Under the null hypothesis of isotropy, a random isotropic point pattern should be expected to have the same value of the directional scalogram for any possible direction. Monte Carlo simulations of the logarithm of the directional scalogram over all directions are used to approximate the test distribution and the critical values. We demonstrate the efficacy of the approach through simulation studies and an application to a desert plant data set, where our approach confirms suspected directional effects in the spatial distribution of the desert plant species.