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Statistica Sinica 25 (2015), 61-79

A BAYESIAN SPATIO-TEMPORAL GEOSTATISTICAL
MODEL WITH AN AUXILIARY LATTICE
FOR LARGE DATASETS
Ganggang Xu1, Faming Liang1 and Marc G. Genton2
1Texas A&M University and 2King Abdullah University of Science and Technology

Abstract: When spatio-temporal datasets are large, the computational burden can lead to failures in the implementation of traditional geostatistical tools. In this paper, 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 observations 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 proposed model is illustrated using simulation studies and a dataset of precipitation data from the coterminous United States.

Key words and phrases: Auxiliary Lattice, Bayesian hierarchical spatio-temporal model, Gaussian Markov random field, large datasets, spatio-temporal kriging.

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