Keywords: Spatial data, Gaussian process, bootstrap, nearest neighbors, maximum likelihood estimate (mle), numerical optimization, sparse Cholesky factors, computational complexity, satellite temperature data.
Analysis of geostatistical data through spatial process model necessitates computation and storage that becomes prohibitive with the increment in number of spatial locations. Inference on the spatial covariance parameters is often critical to scientists for understanding the structural dependence in the data. For spatial Gaussian process regression, finite sample inference proceeds either using posterior distributions from a fully Bayesian approach or via resampling or subsampling techniques in a frequentist setting. Resampling methods, in particular the bootstrap, have become more attractive in the modern age of big data as, unlike Bayesian models which require sequentially sampling from a Markov Chain Monte Carlo, they naturally lend themselves to parallel computing resources. However, spatial bootstrap involves an expensive Cholesky decomposition to decorrelate the data. In this manuscript, we develop a highly scalable parametric spatial bootstrap that uses sparse Cholesky factors for parameter estimation and decorrelation. The proposed BRISC algorithm requires linear memory and computations, and is embarrassingly parallel, thereby delivering massive scalability. Simulation studies highlight the accuracy and computational efficiency of our approach. Analyzing a massive satellite temperature data, BRISC produces inference that closely matches that delivered from a state-of-the-art Bayesian approach, while being several times faster. The R-package BRISC is now available for download from GitHub (https://github.com/ArkajyotiSaha/BRISC) and it will be available on CRAN soon.