A Bayesian INLA-SPDE Approach to Spatio-Temporal Point-Grid Fusion with Change-of-Support and Misaligned Covariates

2025-11-18

AI Summary

This study addresses the challenge of continuous spatiotemporal prediction arising from spatial support mismatch between point observations and gridded data, as well as spatiotemporal misalignment of covariates. We propose a hierarchical Bayesian spatiotemporal fusion framework. Methodologically, we formulate a latent Gaussian field model grounded in the Matérn stochastic partial differential equation (SPDE) prior to jointly integrate heterogeneous multi-source data; we innovatively enable joint modeling of misaligned covariates and achieve efficient Bayesian inference via integrated nested Laplace approximation (INLA) coupled with the SPDE approach. Applied to daily soil moisture prediction across Scotland, the framework produces high-resolution continuous spatiotemporal maps, significantly outperforming single-source models in accuracy while delivering full uncertainty quantification. It establishes a scalable, interpretable statistical modeling paradigm for cross-scale environmental monitoring.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We propose a spatio-temporal data-fusion framework for point data and gridded data with variables observed on different spatial supports. A latent Gaussian field with a Matérn-SPDE prior provides a continuous space representation, while source-specific observation operators map observations to both point measurements and gridded averages, addressing change-of-support and covariate misalignment. Additionally incorporating temporal dependence enables prediction at unknown locations and time points. Inference and prediction are performed using the Integrated Nested Laplace Approximation and the Stochastic Partial Differential Equations approach, which delivers fast computation with uncertainty quantification. Our contributions are: a hierarchical model that jointly fuses multiple data sources of the same variable under different spatial and temporal resolutions and measurement errors, and a practical implementation that incorporates misaligned covariates via the same data fusion framework allowing differing covariate supports. We demonstrate the utility of this framework via simulations calibrated to realistic sensor densities and spatial coverage. Using the simulation framework, we explore the stability and performance of the approach with respect to the number of time points and data/covariate availability, demonstrating gains over single-source models through point and gridded data fusion. We apply our framework to soil moisture mapping in the Elliot Water catchment (Angus, Scotland). We fuse in-situ sensor data with aligned and misaligned covariates, satellite data and elevation data to produce daily high resolution maps with uncertainty.

Problem

• Fuses point and gridded data with different spatial supports
• Addresses misaligned covariates and change-of-support issues
• Enables spatio-temporal prediction at unknown locations with uncertainty quantification

Innovation

• Bayesian INLA-SPDE for spatio-temporal fusion
• Hierarchical model fuses multi-resolution data sources
• Handles misaligned covariates with unified framework