A Bayesian Geoadditive Model for Spatial Disaggregation

TL;DR

This paper introduces a Bayesian spatial disaggregation model for count data that combines flexible covariate effects, efficient computation via Laplace approximation, and applicability to high-resolution disease risk mapping.

Contribution

It develops a novel Bayesian model integrating penalized splines and low-rank kriging with Laplace approximation for scalable, flexible spatial disaggregation of count data.

Findings

Both estimation strategies perform well in simulations.

The approximate method offers significant computational gains.

Application to UK and Belgium disease data demonstrates practical utility.

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.