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November 2013 Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm
Peter J. Diggle, Paula Moraga, Barry Rowlingson, Benjamin M. Taylor
Statist. Sci. 28(4): 542-563 (November 2013). DOI: 10.1214/13-STS441

Abstract

In this paper we first describe the class of log-Gaussian Cox processes (LGCPs) as models for spatial and spatio-temporal point process data. We discuss inference, with a particular focus on the computational challenges of likelihood-based inference. We then demonstrate the usefulness of the LGCP by describing four applications: estimating the intensity surface of a spatial point process; investigating spatial segregation in a multi-type process; constructing spatially continuous maps of disease risk from spatially discrete data; and real-time health surveillance. We argue that problems of this kind fit naturally into the realm of geostatistics, which traditionally is defined as the study of spatially continuous processes using spatially discrete observations at a finite number of locations. We suggest that a more useful definition of geostatistics is by the class of scientific problems that it addresses, rather than by particular models or data formats.

Citation

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Peter J. Diggle. Paula Moraga. Barry Rowlingson. Benjamin M. Taylor. "Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm." Statist. Sci. 28 (4) 542 - 563, November 2013. https://doi.org/10.1214/13-STS441

Information

Published: November 2013
First available in Project Euclid: 3 December 2013

zbMATH: 1331.86027
MathSciNet: MR3161587
Digital Object Identifier: 10.1214/13-STS441

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.28 • No. 4 • November 2013
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