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

TLDR

Geostatistics traditionally studies spatially continuous processes using spatially discrete observations at a finite number of locations, and problems of this kind fit naturally into that realm. We propose redefining geostatistics by the scientific problems it addresses rather than by specific models or data formats. We introduce log‑Gaussian Cox processes as models for spatial and spatio‑temporal point processes, discuss inference challenges, and illustrate their application through four case studies. The LGCP framework proves useful for estimating intensity surfaces, detecting spatial segregation in multi‑type processes, mapping disease risk from discrete data, and enabling real‑time health surveillance.

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.