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Blur-generated non-separable space-time models.

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Blur-generated non-separable space-time models. / Brown, P. E.; Kaaresn, K. F.; Roberts, G. O. et al.
In: Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 62, No. 4, 2000, p. 847-860.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Brown, PE, Kaaresn, KF, Roberts, GO & Tonellato, S 2000, 'Blur-generated non-separable space-time models.', Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 62, no. 4, pp. 847-860. https://doi.org/10.1111/1467-9868.00269

APA

Brown, P. E., Kaaresn, K. F., Roberts, G. O., & Tonellato, S. (2000). Blur-generated non-separable space-time models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62(4), 847-860. https://doi.org/10.1111/1467-9868.00269

Vancouver

Brown PE, Kaaresn KF, Roberts GO, Tonellato S. Blur-generated non-separable space-time models. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2000;62(4):847-860. doi: 10.1111/1467-9868.00269

Author

Brown, P. E. ; Kaaresn, K. F. ; Roberts, G. O. et al. / Blur-generated non-separable space-time models. In: Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2000 ; Vol. 62, No. 4. pp. 847-860.

Bibtex

@article{8b0d015c5ed8439c91d5c9b5195bc439,
title = "Blur-generated non-separable space-time models.",
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.",
keywords = "Blurring • Continuous time • Infinitely divisible functions",
author = "Brown, {P. E.} and Kaaresn, {K. F.} and Roberts, {G. O.} and S. Tonellato",
year = "2000",
doi = "10.1111/1467-9868.00269",
language = "English",
volume = "62",
pages = "847--860",
journal = "Journal of the Royal Statistical Society: Series B (Statistical Methodology)",
issn = "1369-7412",
publisher = "Wiley-Blackwell",
number = "4",

}

RIS

TY - JOUR

T1 - Blur-generated non-separable space-time models.

AU - Brown, P. E.

AU - Kaaresn, K. F.

AU - Roberts, G. O.

AU - Tonellato, S.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

KW - Blurring • Continuous time • Infinitely divisible functions

U2 - 10.1111/1467-9868.00269

DO - 10.1111/1467-9868.00269

M3 - Journal article

VL - 62

SP - 847

EP - 860

JO - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

JF - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

SN - 1369-7412

IS - 4

ER -