Assessing Spatial Stationarity and Segmenting Spatial Processes into Stationary Components

TL;DR

This paper introduces a new visualization and segmentation method for nonstationary spatial data using a stable covariance parameter, fused lasso, and Voronoi tessellations, validated through simulations and real data.

Contribution

We develop a novel approach combining a stable microergodic parameter, fused lasso, and Voronoi tessellations to analyze and segment nonstationary spatial processes with a single realization.

Findings

Effective visualization of nonstationarity in geostatistics

Successful segmentation into stationary sub-regions

Robust stationarity testing method demonstrated

Abstract

In this research, we propose a novel technique for visualizing nonstationarity in geostatistics, particularly when confronted with a single realization of data at irregularly spaced locations. Our method hinges on formulating a statistic that tracks a stable microergodic parameter of the exponential covariance function, allowing us to address the intricate challenges of nonstationary processes that lack repeated measurements. We implement the fused lasso technique to elucidate nonstationary patterns at various resolutions. For prediction purposes, we segment the spatial domain into stationary sub-regions via Voronoi tessellations. Additionally, we devise a robust test for stationarity based on contrasting the sample means of our proposed statistics between two selected Voronoi subregions. The effectiveness of our method is demonstrated through simulation studies and its application to a precipitation dataset in Colorado.