  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.
