Coherent disaggregation and uncertainty quantification for spatially misaligned data

Abstract

This thesis addresses the challenge of spatial misalignment in spatial models defined over continuous domains, with a particular emphasis on quantifying uncertainty that arises from data disaggregation. A central methodological contribution is the extension of nonlinear predictors within the Integrated Nested Laplace Approximation (INLA) framework. This is achieved by formulating INLA as a Bayesian optimisation procedure applied in an iterative manner, where linearisation points are evaluated using an appropriate metric until a convergence criterion is satisfied.

We provide theoretical guarantees showing that the approximation error resulting from the linearisation of the nonlinearity arising due to spatial misalignment is bounded by terms of higher order, provided that the linearisation points are sufficiently localised. The proposed approach effectively captures the nonlinearity induced by spatial misalignment and accurately recovers the underlying intensity fields for both aggregated count data and point pattern observations, whether represented in raster or areal format. The methodology is further extended to account for partially observed data, a common feature of aggregated datasets. Simulation studies demonstrate that including uncertainty terms in both joint and two stage modelling frameworks leads to substantial improvements in predictive accuracy and inferential reliability, as measured by proper scoring rules.

The methodology is applied to a large-scale landslide inventory triggered by the 2015 Mᵥᵥ 7.8 Gorkha Earthquake in Nepal. A novel application is the use of pixel-based geomorphological covariates, notably the slope steepness metric, Channel Steepness Index (kₛₙ), derived objectively from remotely sensed Digital Elevation Model (DEM) data. Compared to traditional slope unit polygon approaches, this pixel-based method is computationally efficient and more objective. Model comparisons using strictly proper scoring rules identify kₛₙ as a key triggering factor, outperforming conventional covariates such as land cover and Peak Ground Acceleration (PGA). Additionally, flow distance to the nearest channel is found to better predict landslide size and location than sheer relief to channel. Covariate influence is quantified using the Coefficient of Variation (cᵥ), providing interpretable measures of relative spatial variability.

Collectively, this thesis advances continuous spatial modelling by developing tools that explicitly address spatial misalignment and incorporate uncertainty quantification. These contributions enhance predictive accuracy and interpretability in geoscientific applications, with broad implications for environmental risk assessment and hazard modelling.