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Blur-generated non-separable space-time models.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

  • P. E. Brown
  • K. F. Kaaresn
  • G. O. Roberts
  • S. Tonellato
<mark>Journal publication date</mark>2000
<mark>Journal</mark>Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Issue number4
Number of pages14
Pages (from-to)847-860
Publication StatusPublished
<mark>Original language</mark>English


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.