Statistical Inferences and Predictions for Areal Data and Spatial Data Fusion with Hausdorff–Gaussian Processes

Abstract Accurate modeling of spatial dependence is pivotal for both parameter estimation and prediction in spatial data analysis. The spatial structure of the data significantly narrows the set of available models. Existing areal data models often ignore polygon geometry, while data fusion models require computationally intensive integration, limiting their application. In response to these issues, we propose the Hausdorff–Gaussian process (HGP), a versatile model utilizing the Hausdorff distance to capture spatial dependence in both point and areal data. Integration into generalized linear mixed-effects models enhances its applicability, particularly in addressing data fusion challenges. We validate our approach through a comprehensive simulation study and application to two real-world scenarios: one involving areal data and another demonstrating its effectiveness in data fusion. Results show the HGP is a competitive, flexible, and robust solution for modeling diverse spatial data, with potential applications in fields like public health and climate science. Supplementary materials accompanying this paper appear online.