Detecting changes in the mean of spatial random fields on a regular grid

TL;DR

This paper introduces new statistical methods for detecting changes in the mean of spatial random fields on regular grids, including tests based on Gini's mean difference and a variance-based approach, with proven asymptotic properties and practical effectiveness demonstrated through simulations and satellite image analysis.

Contribution

It extends change detection techniques to spatial data, developing two novel test statistics and a de-correlation algorithm for dependent data, with theoretical guarantees and real-world application.

Findings

Both tests maintain proper size and power in simulations.

The variance-based test reliably detects deforestation regions.

Methods are effective for both independent and dependent spatial data.

Abstract

We propose statistical procedures for detecting changes in the mean of spatial random fields observed on regular grids. The proposed framework provides a general approach to change detection in spatial processes. Extending a block-based method originally developed for time series, we introduce two test statistics, one based on Gini's mean difference and a novel variance-based variant. Under mild moment conditions, we derive asymptotic normality of the variance-based statistic and prove its consistency against almost all non-constant mean functions (in a sense of positive Lebesgue measure). To accommodate spatial dependence, we further develop a de-correlation algorithm based on estimated autocovariances. Monte Carlo simulations demonstrate that both tests maintain appropriate size and power for both independent and dependent data. In an application to satellite images, especially our variance-based test reliably detects regions undergoing deforestation.