Details
Date: April 10, 2024
Location: Storrs, CT
Abstract
Accurate modeling of spatial dependence is crucial for analyzing spatial and spatiotemporal data, as it directly influences parameter estimation and prediction accuracy. The unique structure and geometry of spatial data demand tailored approaches for valid statistical inference. Traditional areal data models, often reliant on adjacency matrices, may not adequately capture the nuances of polygons with varying sizes and shapes. Data fusion models, while effective, can become computationally prohibitive for even moderately large datasets due to their reliance on intensive numerical integrals.
To address these challenges, we propose the Hausdorff-Gaussian Process~(HGP), a flexible model class that employs the Hausdorff distance to quantify spatial dependence in both point and areal data. We establish a valid correlation function for the HGP, facilitating its use in diverse modeling techniques, including geostatistical and areal models. Seamless integration into generalized linear mixed-effects models expands its applicability, making it particularly well-suited for tackling change of support and data fusion problems.
Our comprehensive simulation study and applications to three real-world datasets validate the HGP’s efficacy. Applications with both areal and fused spatial data demonstrate our model’s capabilities. Additionally, we adapt the HGP for spatiotemporal modeling of areal Tuberculosis data using a separable model. Results indicate that the HGP delivers competitive goodness-of-fit and prediction performance compared to specialized models. In conclusion, the HGP provides a versatile and robust framework for modeling spatial data across various types and geometries, holding significant promise for applications in fields like public health and climate science.