Scalable Computations for Nonstationary Gaussian Processes

2022/06/10 by Paul G. Beckman, Beckman, Paul G., Christopher J. Geoga +5 · 1 citation
Earth and Planetary Sciences · Environmental Science · #Atmospheric and Environmental Gas Dynamics #Computation (stat.CO) #FOS: Computer and information sciences #Marine and coastal ecosystems #Soil Geostatistics and Mapping

paper · pdf · doi:10.48550/arxiv.2206.05220

openalex publication_date 2022/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with conventional dense linear algebra. In addition, derivative-free or even first-order optimization methods can be slow to converge when estimating many spatially varying parameters. We present here a computational framework that couples an algebraic block-diagonal plus low-rank covariance matrix approximation with stochastic trace estimation to facilitate the efficient use of second-order solvers for maximum likelihood estimation of Gaussian process models with many parameters. We demonstrate the effectiveness of these methods by simultaneously fitting 192 parameters in the popular nonstationary model of Paciorek and Schervish using 107,600 sea surface temperature anomaly measurements.

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