Kryging: Geostatistical analysis of large-scale datasets using Krylov subspace methods

TL;DR

Kryging introduces a scalable, efficient method for geostatistical analysis of large spatial datasets using Krylov subspace techniques, enabling fast covariance estimation and spatial prediction with uncertainty quantification.

Contribution

The paper presents Kryging, a novel approximate inference approach that leverages Krylov subspace methods and Toeplitz structures for scalable Gaussian process analysis of large spatial datasets.

Findings

Effective in handling large datasets with reduced computation time

Performs well across various sampling designs and parameter settings

Demonstrated success on real satellite temperature data

Abstract

Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present a novel approximate inference methodology that uses profile likelihood and Krylov subspace methods to estimate the spatial covariance parameters and makes spatial predictions with uncertainty quantification. The proposed method, Kryging, applies for both observations on regular grid and irregularly-spaced observations, and for any Gaussian process with a stationary covariance function, including the popular $\Matern$ covariance family. We make use of the block Toeplitz structure with Toeplitz blocks of the covariance matrix and use fast Fourier transform methods to alleviate the computational and memory bottlenecks. We perform extensive simulation studies to show the effectiveness of our model by varying sample sizes, spatial parameter values and sampling designs. A real data application is also performed on a dataset consisting of land surface temperature readings taken by the MODIS satellite. Compared to existing methods, the proposed method performs satisfactorily with much less computation time and better scalability.