Integrating machine learning and Bayesian nonparametrics for flexible modeling of point pattern data

Two common approaches to analyze point pattern (location-only) data are mixture models and log-Gaussian Cox processes. The former provides a flexible model for the intensity surface at the expense of no covariate effect estimates while the latter estimates covariate effects at the expense of computation. A bridge is built between these two methods that leverages the strengths of both approaches. Namely, Bayesian nonparametrics are first used to flexibly model the intensity surface. The posterior draws of the fitted intensity surface are then transformed into the equivalent representation under the log-Gaussian Cox process approach. Using principles of machine learning, estimates of covariate effects are obtained. The proposed two-step approach results in accurate estimates of parameters, with proper uncertainty quantification, which is illustrated with real and simulated examples.