Bayesian Multiresolution Modeling Of Georeferenced Data

TL;DR

This paper introduces an extended multiresolution Bayesian spatial model for non-Gaussian data, improving inference robustness and prediction accuracy over existing methods, demonstrated on Kenyan education data.

Contribution

It develops the extended LatticeKrig (ELK) model with interpretable priors, enhancing multiscale spatial analysis for non-Gaussian responses using INLA.

Findings

ELK shows modest improvement in spatial smoothing and prediction.

Differences between models increase with distance from observations.

Model robustness is improved through prior specification and parameter integration.

Abstract

Current implementations of multiresolution methods are limited in terms of possible types of responses and approaches to inference. We provide a multiresolution approach for spatial analysis of non-Gaussian responses using latent Gaussian models and Bayesian inference via integrated nested Laplace approximation (INLA). The approach builds on `LatticeKrig', but uses a reparameterization of the model parameters that is intuitive and interpretable so that modeling and prior selection can be guided by expert knowledge about the different spatial scales at which dependence acts. The priors can be used to make inference robust and integration over model parameters allows for more accurate posterior estimates of uncertainty. The extended LatticeKrig (ELK) model is compared to a standard implementation of LatticeKrig (LK), and a standard Mat\'ern model, and we find modest improvement in spatial oversmoothing and prediction for the ELK model for counts of secondary education completion for women in Kenya collected in the 2014 Kenya demographic health survey. Through a simulation study with Gaussian responses and a realistic mix of short and long scale dependencies, we demonstrate that the differences between the three approaches for prediction increases with distance to nearest observation.