Statistical Science

Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm

Peter J. Diggle, Paula Moraga, Barry Rowlingson, and Benjamin M. Taylor

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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.

Article information

Source
Statist. Sci., Volume 28, Number 4 (2013), 542-563.

Dates
First available in Project Euclid: 3 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.ss/1386078878

Digital Object Identifier
doi:10.1214/13-STS441

Mathematical Reviews number (MathSciNet)
MR3161587

Zentralblatt MATH identifier
1331.86027

Keywords
Cox process epidemiology geostatistics Gaussian process spatial point process

Citation

Diggle, Peter J.; Moraga, Paula; Rowlingson, Barry; Taylor, Benjamin M. Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm. Statist. Sci. 28 (2013), no. 4, 542--563. doi:10.1214/13-STS441. https://projecteuclid.org/euclid.ss/1386078878


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Supplemental materials

  • Supplementary material: Supplementary materials for “Spatial and spatio-temporal log-Gaussian Cox processes: Extending the geostatistical paradigm”. This material contains mixing, convergence and inferential diagnostics for all of the examples in the main article and is also available from http://www.lancs.ac.uk/staff/taylorb1/statsciappendix.pdf.