The article discusses methods used to manage large spatial datasets, particularly emphasizing Gaussian Process (GP) regression where covariance matrix inversion presents a significant computational challenge. Various strategies are explored, including low-rank approximations, covariance tapering, and Vecchia-type methods. These approaches aim to enhance efficiency while retaining the structural integrity of GP models. Empirical studies, including analysis of global ocean temperature data, showcase the effectiveness of these techniques, offering a comprehensive understanding of their computational benefits in statistical methodologies applicable to environmental data analysis.
The computational challenge in Gaussian Process regression largely stems from the need to efficiently handle the inverse of the covariance matrix, which can be addressed through various approximation methods.
Low-rank approximations provide a viable strategy by projecting high-dimensional processes onto a lower-dimensional space, facilitating more efficient approximations while preserving the essence of the original spatial process.
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