A Bayesian Spatio-Temporal Geostatistical Model with an Auxiliary Lattice for Large Datasets

When facing spatio-temporal datasets of massive size, the aggravated computational burden can often lead to failures in the implementations of traditional spatial statistical tools. In this paper, we propose a computationally efficient Bayesian hierarchical spatio-temporal model where the spatial dependence is approximated by a Gaussian Markov random field while the temporal correlation is described using a vector autoregressive model. By introducing an auxiliary lattice on the spatial region of interest, the proposed method not only can handle irregularly spaced observations in the spatial domain but can also nicely bypass the missing data problem in a spatio-temporal process. Because the computational complexity of the proposed Markov chain Monte Carlo algorithm is of the order O(n) with n being the total number of observations in space and time, our method can be used to handle very-large-to-massive spatio-temporal datasets with reasonable CPU times. The predictive performance of the proposed model is illustrated using simulation studies and a real-world dataset of precipitation data for the coterminous United States.