Approximate inference for disease mapping with sparse Gaussian processes.

Area of Science:

• Spatial statistics
• Computational epidemiology
• Geospatial modeling

Background:

• Gaussian process (GP) models are valuable for disease mapping due to their ability to model spatial correlations.
• However, standard GP models face computational and memory challenges, especially with non-Gaussian observation models, hindering inference.

Purpose of the Study:

• To address the computational burden and inference difficulties in Gaussian process models for disease mapping.
• To develop efficient sparse approximations and approximate inference methods for GPs.

Main Methods:

• Implemented fully and partially independent conditional (FIC/PIC) sparse approximations for GPs in two-dimensional surfaces.
• Utilized expectation propagation (EP) and Laplace approximation (LA) for approximate posterior inference.
• Proposed combining FIC with compactly supported covariance functions for efficient additive models.

Main Results:

• Sparse GP approximations significantly speed up computations and reduce memory requirements.
• EP and LA provide fast and accurate posterior inference, comparable to Markov Chain Monte Carlo (MCMC).
• The proposed additive model effectively captures both long and short-range spatial correlations.

Conclusions:

• The developed sparse GP approximations and inference methods offer a computationally efficient solution for disease mapping.
• These techniques overcome the limitations of traditional GP models, enabling faster and more scalable spatial analysis.
• The approach enhances the practical applicability of GPs in epidemiological studies.