A Bayesian Geoadditive Model for Spatial Disaggregation

2025-07-22

AI Summary

This paper addresses the challenge of modeling count data under high-resolution spatial discretization, where existing methods often neglect nonlinear covariate effects and spatial dependence. We propose a flexible and computationally efficient Bayesian geostatistical additive model. Methodologically, it integrates penalized splines to capture nonlinear covariate effects and low-rank spline-based kriging to model spatial random effects, with inference accelerated via Laplace approximation. The framework supports both exact likelihood and spatially aggregated (discretized) likelihood estimation. Our key contribution lies in unifying the treatment of nonlinearity, spatial correlation, and areal aggregation—achieving both statistical accuracy and scalability. In empirical applications mapping disease incidence rates across the UK and Belgium, the method produces high-resolution risk surfaces. Simulation studies confirm its estimation accuracy, while the Laplace approximation improves computational efficiency by several orders of magnitude compared to standard Markov chain Monte Carlo approaches.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Bayesian Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We present a novel Bayesian spatial disaggregation model for count data, providing fast and flexible inference at high resolution. First, it incorporates non-linear covariate effects using penalized splines, a flexible approach that is not typically included in existing spatial disaggregation methods. Additionally, it employs a spline-based low-rank kriging approximation for modeling spatial dependencies. The use of Laplace approximation provides computational advantages over traditional Markov Chain Monte Carlo (MCMC) approaches, facilitating scalability to large datasets. We explore two estimation strategies: one using the exact likelihood and another leveraging a spatially discrete approximation for enhanced computational efficiency. Simulation studies demonstrate that both methods perform well, with the approximate method offering significant computational gains. We illustrate the applicability of our model by disaggregating disease rates in the United Kingdom and Belgium, showcasing its potential for generating high-resolution risk maps. By combining flexibility in covariate modeling, computational efficiency and ease of implementation, our approach offers a practical and effective framework for spatial disaggregation.

Problem

• Develops Bayesian model for high-resolution spatial count data
• Incorporates non-linear covariate effects via penalized splines
• Enables efficient large-scale spatial disaggregation with Laplace approximation

Innovation

• Bayesian spatial disaggregation with penalized splines
• Spline-based low-rank kriging for spatial dependencies
• Laplace approximation for computational efficiency