Going off grid: Computationally efficient inference for log-Gaussian Cox processes

In this paper we introduce a new method for performing computational inference on log-Gaussian Cox processes (LGCP). Contrary to current practice, we do not approximate by a counting process on a partition of the domain, but rather attack the point process likelihood directly. In order to do this, we use the continuously specified Markovian random fields introduced by Lindgren et al. (2011). The inference is performed using the R-INLA package of Rue et al. (2009), which allows us to perform fast approximate inference on quite complicated models. The new method is tested on a real point pattern data set as well as two interesting extensions to the classical LGCP framework. The first extension considers the very real problem of variable sampling effort throughout the observation window and implements the method of Chakraborty et al. (Submitted). The second extension moves beyond what is possible with current techniques and constructs a log-Gaussian Cox process on the world's oceans.