A Bayesian spatio-temporal geostatistical model with an auxiliary lattice for large datasets

Abstract

When spatio-temporal datasets are large, the computational burden can lead to failures in the implementation of traditional geostatistical tools. In this pa- per, we propose a computationally efficient Bayesian hierarchical spatio-temporal model in which the spatial dependence is approximated by a Gaussian Markov random field (GMRF) 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 is not only able to handle irregularly spaced observa- tions in the spatial domain, but it is also able to 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 the total number of observations in space and time, our method can be used to handle very large spatio-temporal datasets with reasonable CPU times. The performance of the pro- posed model is illustrated using simulation studies and a dataset of precipitation data from the coterminous United States.