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Abstract:
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One of the challenges in spatio-temporal modeling is how to manage the large amount of missing information. Data augmentation techniques are used to infer about missing values, unobserved or latent processes, approximation of continuous time processes that are discretely observed. In this paper we discuss Bayesian inference for the stochastic differential equations (SDE) in a spatial context, using a data augmentation approach. We propose some methods to model space time data as noisy realizations of an underlying system of nonlinear SDEs. The parameters of this system are realizations of spatially correlated Gaussian processes. We provide an algorithm, the conditional innovation scheme, that helps to overcome some of the difficulties in the estimation. Our algorithm can be actually applied in any general multivariate SDE setting. Examples to illustrate the methodology are provided.
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