Scalable computations for nonstationary Gaussian processes

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