Analyzing massive spatial datasets using a Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental health. 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 for point-referenced spatial data. “Kryging” combines Kriging and Krylov subspace methods and applies for both observations on regular grid and irregularly spaced observations, and for any Gaussian process with a stationary isotropic (and certain geometrically anisotropic) covariance function, including the popular Matérn covariance family. We make use of the block Toeplitz structure with Toeplitz blocks of the covariance matrix and use fast Fourier transform methods to bypass the computational and memory bottlenecks of approximating log-determinant and matrix-vector products. 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.
Majumder, S., Guan, Y., Reich, B. J., & Saibaba, A. K. (2022). Kryging: geostatistical analysis of large-scale datasets using Krylov subspace methods. Statistics and Computing, 32(5). https://doi.org/10.1007/s11222-022-10104-3
The authors were partially supported by the National Science Foundation through the awards DMS-1845406 and DMS-1638521. The authors were also partially supported by the National Institute of Health through the awards R01ES031651-01 and R01ES027892 and by The King Abdullah University of Science and Technology grant 3800.2. We would like to thank them for their support.