🤖 AI Summary
To address scale misalignment and information loss in spatial data arising from aggregation or registration, this paper proposes a Bayesian decomposition framework that maps misaligned observations—including point patterns and aggregated counts—onto a continuous spatial domain, enabling uncertainty-aware inversion under four covariate scenarios. We introduce an INLA-driven iterative linearization integration algorithm and design three covariate field reconstruction strategies: Value Plugin, Joint Uncertainty, and Uncertainty Plugin—explicitly propagating uncertainty while maintaining robustness to model misspecification. The method integrates point processes, hierarchical modeling, and multi-source covariates (raster, polygon, and point). In landslide susceptibility mapping, it substantially improves spatial resolution and predictive reliability. Notably, even under covariate scarcity, the Uncertainty Plugin maintains high accuracy, outperforming conventional interpolation and deterministic inversion approaches.
📝 Abstract
Spatial misalignment problems arise from both data aggregation and attempts to align misaligned data, leading to information loss. We propose a Bayesian disaggregation framework that links misaligned data to a continuous domain model using an iteratively linearised integration method via integrated nested Laplace approximation (INLA). The framework supports point pattern and aggregated count models under four covariate field scenarios: extit{Raster at Full Resolution (RastFull), Raster Aggregation (RastAgg), Polygon Aggregation (PolyAgg), and Point Values (PointVal)}. The first three involve aggregation, while the latter two have incomplete fields. For PolyAgg and PointVal, we estimate the full covariate field using extit{Value Plugin, Joint Uncertainty, and Uncertainty Plugin} methods, with the latter two accounting for uncertainty propagation. These methods demonstrate superior performance, and remain more robust even under model misspecification (i.e. modelling a nonlinear field as linear). In landslide studies, landslide occurrences are often aggregated into counts based on slope units, reducing spatial detail. The results indicate that point pattern observations and full-resolution covariate fields should be prioritized. For incomplete fields, methods incorporating uncertainty propagation are preferred. This framework supports landslide susceptibility and other spatial mapping, integrating seamlessly with INLA-extension packages.