Nonparametric density estimation on complex domains using manifold-aware Bayesian additive tree models

Density or intensity function estimation for point pattern data observed on complex domains finds wide applications in spatial data analysis. However, many existing popular density estimation methods face challenges when domains have irregular boundaries, line network structures, sharp concavities, or interior holes. A nonparametric Bayesian additive ensemble of spanning trees model is developed to model the distribution of event occurrences on complex domains. This model uses a random spanning tree weak learner, which can produce flexible and contiguous domain partitions while respecting its geometry and constraints. The method has the advantage of capturing both varying smoothness and sharp changes in density functions. An efficient exact likelihood-based Bayesian inference algorithm is proposed to estimate the density function with uncertainty measures, leveraging a data thinning strategy combined with Poisson-Gamma conjugacy. Simulation studies on various complex domains demonstrate the advantages of the proposed model over competing methods. The method is further applied to the analysis of basketball shot data and crime locations on a road network.