Computationally efficient nonstationary nearest-neighbor Gaussian process models using data-driven techniques

Due to the increased availability of measurements of various geophysical processes, a need has arisen for statistical methods suitable for the analysis of very large nonstationary spatial data sets. The nearest-neighbor Gaussian process (NNGP) models are one of the latest and most popular Gaussian process-based models, which reduce computational complexity and memory storage. The Bayesian inference is based on the assumption of a parametric covariance function that is often assumed stationary or known. Given that NNGP models are sensitive in the stationary assumption in comparison to other reduction methods, there is a need to build nonstationary covariance functions within the NNGP models. However, the construction of a nonstationary covariance function and/or matrix may be computationally expensive by itself in the presence of big data. In this paper, we develop an efficient two-stage approach that deals with nonstationarity and the computational complexity in the presence of a big spatial data set. We propose a new low-cost data-driven tree-structured partitioning technique to divide the spatial region into distinct subregions. Given the partitions, we construct computationally efficient nonstationary covariance functions for NNGP models. We demonstrate the performance of our approach through simulation experiments and an application to the global Total Ozone Matrix Spectrometer (TOMS) data set, in which the proposed approach performs well in terms of both prediction accuracy and computational complexity.