KGR-SKATER: Spatially clustered kernel graph regression for counting processes.

Area of Science:

• Environmental Statistics
• Biostatistics
• Geospatial Analysis

Background:

• High-dimensional non-Gaussian data present challenges for traditional spatiotemporal modeling.
• Existing models often lack interpretability and parsimony in dependence structures.
• Accurate modeling is crucial for understanding complex environmental and health phenomena.

Purpose of the Study:

• To propose a novel procedure for fitting interpretable and parsimonious spatiotemporal models.
• To handle high-dimensional, non-Gaussian data by estimating spatial and temporal dependence structures separately.
• To demonstrate the model's utility in analyzing real-world environmental health data.

Main Methods:

• Estimation of a graph for spatial dependence and a locally periodic kernel for temporal dependence.
• Combination of spatial and temporal components using a Kronecker product for a separable covariance matrix.
• Dimensionality reduction via spatial clustering and model estimation using integrated nested Laplace approximation (INLA).

Main Results:

• The proposed KGR-SKATER model demonstrates comparable in-sample and out-of-sample fit to reference models for respiratory death data.
• The model exhibits superior coverage properties compared to alternative spatiotemporal models.
• A synthetic case study shows improved forecasting performance, especially for non-stationary time series.

Conclusions:

• The proposed multi-step procedure provides an effective approach for modeling complex spatiotemporal dependencies.
• The method offers better interpretability and forecasting capabilities, particularly for environmental health applications.
• The developed model and procedure are valuable tools for analyzing high-dimensional, non-Gaussian spatiotemporal data.