A Time-Series Model for Areal Data Using Spatially Correlated Gaussian Processes

2025-09-01

AI Summary

This paper addresses the challenge of jointly modeling spatially shared variation and localized temporal dynamics in areal spatiotemporal data. We propose a hierarchical Bayesian model grounded in spatially correlated Gaussian processes. Innovatively, we model time-varying parameters as a stochastic process with a conditional autoregressive (CAR) prior and explicitly incorporate dependence between temporal variability and temporal range, enabling more flexible and interpretable characterization of spatiotemporal evolution. Spatial information is propagated through shared variance components, allowing the model to capture cross-regional common patterns while preserving region-specific temporal trajectories. Bayesian inference is performed via a MALA–MH–Gibbs hybrid MCMC algorithm. Evaluated on real-world datasets—malaria incidence in Mozambique and food insecurity prevalence in Cameroon—the model achieves significantly higher predictive accuracy than conventional approaches, demonstrating clear utility for public health surveillance and policy decision-making.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Machine Learning: Bayesian Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Traditional spatio-temporal models for areal data typically begin with spatial structure imposed at the level of random effects and later extend to include temporal dynamics. We propose an alternative hierarchical modeling framework that captures temporal trends in areal data through Gaussian processes that share spatial information via correlated variance components. This allows the model to better capture shared patterns of variability across regions while preserving local temporal dynamics, offering a more flexible representation of spatio-temporal processes. Specifically, we extend independent Gaussian-process models for time-series data to a spatially correlated framework by placing a conditional autoregressive (CAR) prior on the parameters governing the temporal variability and imposing a conditional dependence of the temporal range on the temporal variance. We apply this model to two case studies: monthly malaria incidence in Niassa, Mozambique, and weekly food insecurity prevalence in Cameroon. Inference is conducted within a Bayesian framework using approximate posterior sampling. Given the hierarchical structure of the model, we employ a combination of Markov chain Monte Carlo (MCMC) techniques, including the Metropolis-adjusted Langevin algorithm (MALA), Metropolis-Hastings, and Gibbs sampling. In both applications, the model demonstrates strong in-sample performance with narrow credible intervals and outperforms established spatio-temporal approaches in many regions when forecasting. These results underscore the model's ability to capture complex spatio-temporal dependencies while maintaining interpretability, key in settings with sparse data and policy relevance. By accounting for spatio-temporal variation through the evolution of temporal dynamics themselves, our approach offers a flexible and principled tool for many applied contexts.

Problem

• Modeling spatio-temporal dependencies in areal data
• Capturing shared variability patterns across regions
• Improving forecasting accuracy for policy-relevant applications

Innovation

• Spatially correlated Gaussian processes for areal data
• Conditional autoregressive prior on temporal parameters
• Bayesian inference with MCMC and MALA sampling