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Blur-generated non-separable space-time models.

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 (Statistical Methodology), 62 (4). pp. 847-860. ISSN 1369-7412

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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.

Item Type: Article
Journal or Publication Title: Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Uncontrolled Keywords: Blurring • Continuous time • Infinitely divisible functions
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Lancaster Environment Centre
ID Code: 19295
Deposited By: ep_ss_importer
Deposited On: 25 Nov 2008 09:10
Refereed?: Yes
Published?: Published
Last Modified: 23 Oct 2014 16:13
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19295

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