BRISC: Bootstrap for rapid inference on spatial covariances

In geostatistics, inference on spatial covariance parameters of the Gaussian process is often critical to scientists for understanding structural dependence in data. Finite-sample inference customarily proceeds either using posterior distributions from fully a Bayesian approach or via resampling/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 that require sequential sampling from Markov chain Monte Carlo, they naturally lend themselves to parallel computing resources. However, a 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 bootstrap for rapid inference on spatial covariances (BRISC) algorithm requires linear memory and computations and is embarrassingly parallel, thereby delivering substantial scalability. Simulation studies highlight the accuracy and computational efficiency of our approach. Analysing large 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 will be available on CRAN soon.