Spatially continuous modelling of aggregated outcome data

2026-04-16

AI Summary

This study addresses the modeling challenge where response variables are observed as aggregates over coarse spatial units (e.g., administrative regions), while covariates are available at fine-grained raster resolutions. The authors propose a block aggregation approach that constructs a linear predictor at fine resolution, incorporating covariate effects and a continuous Gaussian process. Coarse-scale response distributions are then derived via an inverse link function and spatial integration over each aggregate unit. This method departs from conventional centroid- or zonal-aggregation paradigms, enabling reliable inference at arbitrary spatial resolutions while preserving fine-scale mechanistic modeling capabilities and remaining compatible with coarse-grained observations. Empirical evaluations demonstrate that the approach achieves predictive performance comparable to standard models in forecasting wastewater viral concentrations and cardiovascular hospitalization rates, while substantially enhancing flexibility in spatial inference.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

This work develops a block aggregation approach to spatial estimation and prediction when the response is observed at a coarse spatial scale, for example as counts of events in administrative areas, or blocks, while covariates are available at a finer spatial resolution, typically as raster images. Our approach specifies a linear predictor at the finer resolution as a combination of covariate effects and a latent, spatially continuous Gaussian process. This linear predictor then determines the distribution of the response through an inverse link function and spatial integration. We use a simulation study to evaluate the performance of the proposed approach in comparison to two industry standard approaches: a traditional geostatistical model that associates each response with the centroid of its block; and a Markov random field (MRF) approach that aggregates covariate data to block-level. As expected, the differences in performance among the three approaches are small with respect to block-level prediction. The rationale for, and advantage of, the block aggregation approach lies in its delivery of reliable inferences at whatever spatial resolution is required in a particular application. We describe two applications: a linear Gaussian sampling model of wastewater virus concentrations in England, using population density as covariate; and log-linear Poisson model of cardiovascular hospitalisations in England using socio-demographic variables at fine-scale administrative units as covariates.

Problem

• spatial aggregation
• coarse-scale response
• fine-resolution covariates
• spatial prediction
• block-level data

Innovation

• block aggregation
• spatially continuous Gaussian process
• multiscale spatial modeling
• spatial integration
• fine-scale covariates