Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes

The univariate log‐Gaussian Cox process (LGCP) has shown considerable potential for the flexible modelling of the spatial, and more recently, spatiotemporal, intensity functions of planar point patterns within a restricted region in space. Its flexibility and mathematical tractability are partly offset by the need to acquire sensible estimates of the parameters controlling the dependence structure of the Gaussian field given the observed data. The method of minimum contrast, which compares theoretical descriptors of the process with their non‐parametric counterparts in order to obtain the required estimates, is arguably the most popular in practice to date. This article provides a comprehensive set of simulation studies focused on gauging the performance and impact of minimum contrast methods for parameter estimation of these processes. Results indicate that concerns over arbitrariness of implementation of minimum contrast give way to satisfactory practical performance.