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

2025-12-12

AI Summary

This paper addresses the detection of abrupt changes in the mean function of spatial random fields on regular lattices. We propose two novel block-based test statistics: one based on the Gini mean difference and another on variance. We establish, for the first time, the uniform consistency of the variance-based statistic against virtually all non-constant mean functions. To mitigate spatial dependence, we design a spatial decorrelation algorithm grounded in autocovariance estimation. Asymptotic theory confirms the asymptotic normality of the proposed statistics, while Monte Carlo experiments demonstrate robust size control and high power under both independent and dependent spatial settings. Empirical analysis on satellite remote-sensing imagery shows that the variance-based test reliably identifies localized mean shifts—such as deforestation events—without requiring strong parametric assumptions. The method thus provides a theoretically grounded, computationally feasible, and practically effective approach to high-dimensional spatial anomaly detection.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Computer Vision: Remote Sensing / Geospatial AI
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Detecting mean changes in spatial random fields
• Developing statistical tests for spatial change detection
• Applying methods to identify deforestation in satellite imagery

Innovation

• Extends block-based method from time series to spatial fields
• Introduces Gini's mean difference and variance-based test statistics
• Develops de-correlation algorithm using estimated autocovariances