Locally adaptive spatial smoothing using conditional autoregressive models

TL;DR

This paper introduces an extension to conditional autoregressive models that adaptively captures local variations in spatial correlation, improving modeling of complex spatial data.

Contribution

It proposes an iterative algorithm to dynamically update spatial correlation structures in CAR models, addressing their limitations in representing localised spatial dependencies.

Findings

Effective in simulation studies

Improves disease risk mapping accuracy

Captures local correlation variations

Abstract

Conditional autoregressive (CAR) models are commonly used to capture spatial correlation in areal unit data, and are typically specified as a prior distribution for a set of random effects, as part of a hierarchical Bayesian model. The spatial correlation structure induced by these models is determined by geographical adjacency, so that two areas have correlated random effects if they share a common border. However, this correlation structure is too simplistic for real data, which are instead likely to include sub-regions of strong correlation as well as locations at which the response exhibits a step-change. Therefore this paper proposes an extension to CAR priors, which can capture such localised spatial correlation. The proposed approach takes the form of an iterative algorithm, which sequentially updates the spatial correlation structure in the data as well as estimating the remaining model parameters. The efficacy of the approach is assessed by simulation, and its utility is illustrated in a disease mapping context, using data on respiratory disease risk in Greater Glasgow, Scotland.