A MATRIX-FREE METHOD FOR SPATIAL-TEMPORAL GAUSSIAN STATE-SPACE MODELS

This study develops a scalable matrix-free h-likelihood method for spatial-temporal Gaussian state-space models. The state vectors are constructed in such a way that they follow spatial-temporal Gaussian autoregressions that are consistent with the conditional formulation of auto-normal spatial fields. The proposed h-likelihood method provides the same inferences as those obtained from the Kalman filter and residual maximum likelihood analyses. However, for data from a large number of spatial sites, our method has significant computational advantages. Furthermore, we describe inferences in small time steps and indicate how the proposed method can be adapted to other complex spatial-temporal dynamical models based on stochastic partial differential equations. The proposed method applies to data with regularly or irregularly sampled spatial locations. Lastly, we illustrate our method by means of a simulation study and a data example on atmospheric concentrations of total nitrate across eastern North America.