Abstract
We propose a method for analysing inhomogeneous spatio-temporal point process data by extending Baddeley’s et al. (2000) inhomogeneous K-function to the spatio-temporal setting. We develop a non-parametric estimator of the space–time inhomogeneous K-function. We then apply the estimator to data on the spatio-temporal distribution of human campylobacteriosis cases in an area of north-west England and investigate evidence for spatio-temporal clustering and spatio-temporal interaction using tests based on this estimator.
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References
Baddeley AJ, Møller J, Waagpetersen R (2000) Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Stat Neerl 54:329–350
Berman M, Diggle PJ (1989) Estimating weighted integrals of the second-order intensity of a spatial point process. J R Stat Soc 51:81–92
Diggle PJ, Chetwynd AG, Haggkvist R, Morris S (1995) Second-order analysis of space-time clustering. Stat Methods Med Res 4:124–36
Diggle PJ, Zeng P, Durr P (2005) Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK. Appl Stat 54:645–658
Gabriel E, Diggle PJ (2009) Second-order analysis of inhomogeneous spatio-temporal point process data. Stat Neerl 63:43–51
Ripley BD (1976) The second-order analysis of stationary point processes. J Appl Probab 13: 255–266
Ripley BD (1977) Modelling spatial patterns (with discussion). J R Stat Soc 39:172–212
Acknowledgements
We would like to thank Eric Bolton, John Cheesbrough, Paul Fearnhead, Andrew Fox, Steven Gee, Andrew J. H. Leatherbarrow, C. Anthony Hart and Daniel J. Wilson for stimulating discussion on various aspects of this work. This work was funded by the Department for Environment, Food and Rural Affairs as part of the Veterinary Training Research Initiative, and the National Centre for Zoonosis Research.
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Gabriel, E., Diggle, P.J. (2010). Second-Order Analysis of the Spatio-temporal Distribution of Human Campylobacteriosis in Preston, Lancashire. In: Atkinson, P., Lloyd, C. (eds) geoENV VII – Geostatistics for Environmental Applications. Quantitative Geology and Geostatistics, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2322-3_9
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DOI: https://doi.org/10.1007/978-90-481-2322-3_9
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