ABSTRACT
Under the log-Cox point process model assumption, we model the log intensity of the Cox process with a Gaussian linear predictor. In this case, the log-Cox process is known as a log-Gaussian Cox process (LGCP, Møller et al., 1998), and inference can be made using INLA. A Cox process is just a name for a Poisson process with varying intensity; thus we use the Poisson likelihood. The original approach that was used to fit these models in INLA (and other software) divides the study region into cells, which form a lattice, and counts the number of points in each one (Møller and Waagepetersen, 2003). These counts can be modeled using a Poisson likelihood conditional on a Gaussian linear predictor and INLA can be used to fit the model (Illian et al., 2012). This can be done with the techniques already shown in this book.
