A Constructive Spatio-Temporal Approach to Modeling Spatial Covariance

TL;DR

This paper introduces a new method for modeling areal spatial covariance using the stationary distribution of spatio-temporal Markov random walks, providing a principled basis for spatial modeling in ecological and social data.

Contribution

It offers a constructive approach linking spatio-temporal processes to areal spatial models, specifically deriving intrinsic SAR models from Markov random walks.

Findings

Applied to trout genetic variation in stream networks.

Analyzed crime rate spatial patterns in Columbus neighborhoods.

Demonstrated the approach's effectiveness in real-world case studies.

Abstract

I present an approach for modeling areal spatial covariance by considering the stationary distribution of a spatio-temporal Markov random walk. In the areal data case, this stationary distribution corresponds to an intrinsic simultaneous autoregressive (SAR) model for spatial correlation, and provides a principled approach to specifying areal spatial models when a spatio-temporal generating process can be assumed. I apply the approach to a study of spatial genetic variation of trout in a stream network in Connecticut, USA, and a study of crime rates in neighborhoods of Columbus, OH, USA.