On evaluating the Watanabe-Akaike information criteria for Bayesian modelling of point referenced spatial data

Abstract

Bayesian modelling of point referenced data estimates the relationships among geospatial variables and enables predictions at unobserved locations. The Watanabe-Akaike information criterion (WAIC) is a model selection criterion for determining the best model configuration from a set of competing candidate models. However, the traditional formulation of the WAIC assumes conditional independence in the outcome variables, an assumption violated by the spatial dependence often exhibited by point referenced spatial data. Consequently, spatial models for point referenced data violate the conditional independence assumption. To address this problem, this thesis introduces the WAIC_NF, a novel approach employing likelihoods for non-factorisable models that consider conditional dependencies for WAIC calculation.

We apply the WAIC_NF to real-world spatial modelling using the 2018 Nigeria Demographic and Health Survey data, focusing on the coverage of the first-dose of the measles-containing vaccine (MCV1). We construct models with different covariance functions and fit them using the integrated nested Laplace approximation -- stochastic partial differential equation (INLA-SPDE) method. We observe notable differences in the WAIC_NF values, in comparison with the WAIC values computed by default using the R-INLA package. Additionally, we extend our WAIC_NF application to the MCV1 dataset by fitting spatial models with the nearest-neighbour Gaussian process (NNGP) method in Stan, effectively identifying the spatial model with the optimal covariance function specifications for the MCV1 dataset.

This thesis contributes to existing knowledge on model selection methods for point referenced spatial data with the WAIC_NF. Our findings highlight its effectiveness for model selection, particularly when choosing among spatial models with different covariance functions. Its integration with two Bayesian spatial modelling platforms — INLA-SPDE in R and NNGP in Stan — enhances its utility and provides a robust model selection framework for Bayesian modelling of point referenced spatial data.

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Identifiers

ORCID for Ho Man Theophilus Chan: orcid.org/0000-0001-6821-4206

ORCID for Sujit Sahu: orcid.org/0000-0003-2315-3598

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