Rainforest tree point process modelling. We consider a subset of the extensive rainforest **data** set credited to Hubbell et al. (2005)  In the survey area, the locations of all Trichilia tuberculata (a tree species of the Mahogany family) have been measured (see Fig. 7 in App. J). We tackle this spatial point pattern with a log-Gaussian Cox process model, which is an inhomogeneous Poisson process model for count data. The unknown intensity function λ(x) is modelled with a Gaussian process such that f (x) = log λ(x). We model locally constant intensity in subregions by discretising the region into np bins (Møller et al., 1998). This leads to having a Poisson observation model in each bin (see App. J). This model reaches posterior consistency in the limit of bin width going to zero (Tokdar and Ghosh, 2007). The accuracy thus improves with tighter binning. We use a separable Matérn-5/2 GP prior over f (x 1 , x 2 ), and discretise the area into a n × p = 200×100 grid with np = 20000 grid bins, and treat the first dimension as time.