The diffusion-based extension of the Matérn field to space-time
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The Matérn field is the most well known family of covariance functions used for Gaussian processes in spatial models. We build upon the original research of Whittle (1953, 1964) and develop the diffusion-based extension of the Matérn field to space-time (DEMF). We argue that this diffusion-based extension is the natural extension of these processes, due to the strong physical interpretation. The corresponding non-separable spatio-temporal Gaussian process is a spatio-temporal analogue of the Matérn field, with range parameters in space and time, smoothness parameters in space and time, and a separability parameter. We provide a sparse representation based on finite element methods that is well suited for statistical inference.
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