A0897
Title: Gaussian processes and spatial data fusion: Avoiding numerical integration
Authors: Lucas da Cunha Godoy - University of California Santa Cruz (United States) [presenting]
Marcos Prates - Universidade Federal de Minas Gerais (Brazil)
Fernando Quintana - Pontificia Universidad Catolica de Chile (Chile)
Jun Yan - University of Connecticut (United States)
Abstract: Spatial data fusion (SDF) combines data on a single phenomenon collected at different spatial resolutions, such as point-referenced measurements from monitoring stations and areal data from satellites or computer models. Standard models assume both data types are realizations of a common Gaussian process (GP), with real data defined as spatial averages of this process. This approach, however, lacks a closed-form solution and requires numerical integration for approximation. This step is not only computationally expensive but also relies on an arbitrary grid selection, for which there is no consensus on an optimal resolution. As an alternative, a generalization of the isotropic GP used in SDF is proposed. The method defines the covariance function based on a distance between sets, allowing for a direct calculation of covariance between any combination of points and areas. This approach completely bypasses the need for integration. The theoretical conditions are established that ensure the validity of the model, and the method's utility is illustrated using an atmospheric temperature dataset. The proposed methodology offers a computationally efficient and conceptually simple alternative, removing the ambiguity of grid selection and providing a more robust solution for practitioners.
