# Testing the Zonal Stationarity of Spatial Point Processes: Applied to prostate tissues and trees locations

## TL;DR

This paper introduces a new statistical test for assessing the stationarity and isotropy of spatial point patterns, using local spectra and variance analysis, with applications to biological tissues and ecological data.

## Contribution

It proposes a novel test based on local spectra and variance analysis for stationarity and isotropy, including neighborhood and clustering assessments, validated through simulations and real data.

## Key findings

- Test effectively detects nonstationarity in spatial patterns
- Method performs well in simulation studies
- Applied successfully to biological and ecological data

## Abstract

We consider the problem of testing the stationarity and isotropy of a spatial point pattern based on the concept of local spectra. Using a logarithmic transformation, the mechanism of the proposed test is approximately identical to a simple two factor analysis of variance procedure when the variance of residuals is known. This procedure is also used for testing the stationarity in neighborhood of a particular point of the window of observation. The same idea is used in post-hoc tests to cluster the point pattern into stationary and nonstationary sub-windows. The performance of the proposed method is examined via a simulation study and applied in a practical data.