Estimation and model selection for an IDE-based spatio-temporal model

Authors:
Kenneth Scerri;Michael Dewar;Visakan Kadirkamanathan
Affiliations:
Department of Systems and Control Engineering, University of Malta, Msida, MSD, Malta;Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, U.K. and School of Informatics, University of Edinburgh, Edinburgh, Scotland;Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, U.K.
Venue:
IEEE Transactions on Signal Processing
Year:
2009

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Abstract

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.