Rational approximation and intrinsic Gaussian processes
This work provides a practical toolkit for intrinsic GPs, benefiting spatial statisticians and practitioners who need robust and interpretable models for spatial data.
The authors developed a systematic framework for intrinsic Gaussian processes (GPs) that includes practical algorithms and dependence models, addressing the lack of computational tools for intrinsic GPs. Numerical examples demonstrate advantages in robustness, interpretability, and computational efficiency over traditional stationary GPs.
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption has lagged behind traditional, covariance-based approaches, in part because the intrinsic formulation has lacked an accompanying toolkit of computational methods and dependence specifications that facilitate fitting and prediction. We develop here a systematic framework for modeling intrinsic GPs and introduce practical algorithms and dependence/variogram models for modeling, inference and computation that parallel those of traditional, stationary GPs. We explore a close connection between intrinsic GP models and rational approximation, which clarifies the underlying problem structure. Numerical examples illustrate how the new tools can be deployed in practice, highlighting the advantages of intrinsic-field modeling in terms of robustness, interpretability, and computational efficiency.