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The maximum likelihood estimation of a dynamic spatiotemporal model is introduced, centred around the inclusion of a prior arbitrary spatiotemporal neighborhood description. The neighborhood description defines a specific parameterization of the state transition matrix, chosen on the basis of prior knowledge about the system. The model used is inspired by the spatiotemporal ARMA (STARMA) model, but the representation used is based on the standard state-space model. The inclusion of the neighborhood into an expectation-maximization based joint state and parameter estimation algorithm allows for accurate characterization of the spatiotemporal model. The process of including the neighborhood, and the effect it has on the maximum likelihood parameter estimate is described and demonstrated in this paper. [ABSTRACT FROM AUTHOR]

A continuous-in-space, discrete-in-time dynamic spatio-temporal model known as the Integro-Difference Equation (IDE) model is presented in the context of data-driven modeling. A novel decomposition of the IDE is derived, leading to state-space representation that does not couple the number of states with the number of observation locations or the number of parameters. Based on this state-space model, an expectation-maximization (EM) algorithm is developed in order to jointly estimate the IDE model's spatial field and spatial mixing kernel. The resulting modeling framework is demonstrated on a set of examples. [ABSTRACT FROM AUTHOR]