Brown, P. E. and Kaaresn, K. F. and Roberts, G. O. and Tonellato, S. (2000) Blur-generated non-separable space-time models. Journal of the Royal Statistical Society, Series B, 62 (4). pp. 847-860.Full text not available from this repository.
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.
|Journal or Publication Title:||Journal of the Royal Statistical Society, Series B|
|Uncontrolled Keywords:||Blurring • Continuous time • Infinitely divisible functions|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Lancaster Environment Centre|
|Deposited On:||25 Nov 2008 09:10|
|Last Modified:||26 Jul 2012 15:27|
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