Estimation of Parameterized Spatio-Temporal Dynamic Models

Spatio-temporal processes are often high-dimensional, exhibiting complicated variability across space and time. Traditional state-space model approaches to such processes in the presence of uncertain data have been shown to be useful. However, estimation of state-space models in this context is often problematic since parameter vectors and matrices are of high dimension and can have complicated dependence structures. We propose a spatio-temporal dynamic model formulation with parameter matrices restricted based on prior scientific knowledge and/or common spatial models. Estimation is carried out via the expectation-maximization (EM) algorithm or general EM algorithm. Several parameterization strategies are proposed and analytical or computational closed form EM update equations are derived for each. We apply the methodology to a model based on an advection-diffusion partial differential equation in a simulation study and also to a dimension-reduced model for a Palmer Drought Severity Index (PDSI) data set.