Blur-generated non-separable space–time models |
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Authors: | Patrick E. Brown,Gareth O. Roberts,Kjetil F. Kå resen,& Stefano Tonellato |
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Affiliation: | Lancaster University, UK,;Norwegian Computing Centre, Norway,;UniversitàCa' Foscari di Venezia, Italy |
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Abstract: | Statistical space–time modelling has traditionally been concerned with separable covariance functions, meaning that the covariance function is a product of a purely temporal function and a purely spatial function. We draw attention to a physical dispersion model which could model phenomena such as the spread of an air pollutant. We show that this model has a non-separable covariance function. The model is well suited to a wide range of realistic problems which will be poorly fitted by separable models. The model operates successively in time: the spatial field at time t +1 is obtained by 'blurring' the field at time t and adding a spatial random field. The model is first introduced at discrete time steps, and the limit is taken as the length of the time steps goes to 0. This gives a consistent continuous model with parameters that are interpretable in continuous space and independent of sampling intervals. Under certain conditions the blurring must be a Gaussian smoothing kernel. We also show that the model is generated by a stochastic differential equation which has been studied by several researchers previously. |
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Keywords: | Blurring Continuous time Infinitely divisible functions |
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