SPDE-Based Geostatistical and Point Process Models for Environmental and Urban Network Applications

Overview

Spatial data analysis increasingly requires methods that operate on complex domains beyond standard Euclidean settings, including networks constrained by road topologies.

We first develop a framework for bivariate spatial models that incorporates correlated measurement errors. Applied to global Argo oceanographic data, the methodology separates correlation in the nugget effect from the spatial dependence of the latent process. A moving-window analysis demonstrates that accounting for this structure reduces bias and improves uncertainty quantification for joint temperature–salinity prediction.

We then introduce log-Gaussian Cox processes on metric graphs, constructing Whittle–Matérn fields via graph differential operators with computationally efficient likelihood-based inference. The methodology is implemented in the MetricGraph R package and integrated with R-INLA. We apply the approach to traffic accident data on a road network in Al-Ahsa, Saudi Arabia, identifying high-risk segments through excursion set analysis.

Finally, we apply bivariate Gaussian random fields on metric graphs to urban air quality mapping. The model combines Whittle–Matérn fields defined on the road network with a linear model of coregionalization, fitted via integrated nested Laplace approximations. Using mobile monitoring data from London, we first illustrate the univariate approach by modeling NO2 concentrations, then analyze the joint spatial structure of CO2 and NOx using the bivariate specification. We further employ excursion set methods to identify pollution hotspots with quantified uncertainty. To our knowledge, this represents the first application of bivariate Whittle–Matérn fields on a metric graph for air pollution mapping.

Collectively, these contributions advance spatial modeling through methodological improvements in multivariate covariance structures, new model classes for non-Euclidean domains, and computationally efficient workflows for environmental applications.