On nearest-neighbor Gaussian process models for massive spatial data.

Area of Science:

• Geostatistics
• Computational Statistics
• Machine Learning

Background:

• Gaussian Process (GP) models are highly flexible for spatiotemporal data.
• Standard GP models face significant storage and computational challenges with large datasets.

Purpose of the Study:

• To introduce Nearest Neighbor Gaussian Processes (NNGP) as a scalable alternative for large geostatistical datasets.
• To demonstrate the computational efficiency and inferential equivalence of NNGP compared to full GP models.

Main Methods:

• Utilizing local information from nearest neighbors to create a conditional specification of the GP model.
• Equating the NNGP approach to sparse modeling of Cholesky factors for large covariance matrices.
• Exploring a general framework for scalable GPs via sparse local kriging.

Main Results:

• NNGP models achieve scalability by leveraging neighbor sets for conditional model specification.
• The method is shown to be equivalent to sparse Cholesky factor modeling.
• Multivariate analysis confirms NNGP inference is indistinguishable from full GP models, but significantly faster.

Conclusions:

• Nearest Neighbor Gaussian Processes provide a computationally efficient and accurate method for analyzing large spatial datasets.
• The NNGP framework offers a practical solution for previously intractable geostatistical modeling problems.
• A variant for automated neighbor set size selection is proposed, enhancing model usability.