Estimation and Model Selection for an IDE-Based Spatio-Temporal Model

A state space model of the stochastic spatio-temporal integro-difference equation (IDE) is derived. Based on multidimensional sampling theory, the dimensions of the state space and parameter space of the model are identified from the spatial bandwidth of the system and the support of the redistribution kernel of the IDE. When both the bandwidth and the kernel support are unknown, a method to propose a number of state space and parameter space dimensions is presented. These chosen dimensions result in a number of candidate model structures. Bayesian model selection, making use of Bayes factor, the data augmentation algorithm and importance sampling, is then used to identify the model best suited to represent the data in a maximum a posteriori sense.