An Additive Gaussian Process Approximation for Large Spatio-Temporal Data

We propose a new additive spatio-temporal Gaussian process approximation to model complex dependence structures for large spatio-temporal data. The proposed approximation method incorporates a computational-complexity-reduction method and a separable covariant function, which can capture different scales of variation and spatio-temporal interactions. The first component is able to capture nonseparable variation while the second component captures the separable variation of all scales. The Bayesian inference is carried out through a Markov chain Monte Carlo algorithm based on the hierarchical representation of the model. Through this representation we are able to utilize the computational advantages of both components. To demonstrate the inferential and computational benefits of the proposed method, we carry out four different simulation studies as well as a real application that concerns the spatio-temporal measurements of ground-level ozone in the Eastern United States.