Details
Date: Aug 4, 2024
Location: Portlant, OR
Abstract
Accurate modeling of spatial dependence is pivotal in analyzing spatial data, influencing parameter estimation and out-of-sample predictions. The spatial structure and geometry of the data significantly impact valid statistical inference. Existing models for areal data often rely on adjacency matrices, struggling to differentiate between polygons of varying sizes and shapes. Conversely, data fusion models, while effective, rely on computationally intensive numerical integrals, presenting challenges for moderately large datasets. In response to these issues, we propose the Hausdorff-Gaussian process (HGP), a versatile model class utilizing the Hausdorff distance to capture spatial dependence in both point and areal data. We introduce a valid correlation function within the HGP framework, accommodating diverse modeling techniques, including geostatistical and areal models. Integration into generalized linear mixed-effects models enhances its applicability, particularly in addressing change of support and 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. The results suggest that the HGP is competitive with specialized models regarding goodness-of-fit and prediction performances. In summary, the HGP offers a flexible and robust solution for modeling spatial data of various types and shapes, with potential applications spanning fields such as public health and climate science.