Bayesian additive regression trees in spatial data analysis with sparse observations

Recently, the Bayesian additive regression trees (BART) model has been one of the most widely used methods in the field of Bayesian nonparametrics. The spatially adjusted BART model was proposed in 2007; however, it has a limited number of applications in spatial data analysis. We propose a new version of the BART model for spatial data analysis tailored to a setting with sparse spatial observations and high-dimensional predictors. Specifically, an adjacency-based weight matrix in a conditional autoregressive prior is replaced by a new definition of weight matrix reflecting any type of spatial structures, and selection probabilities on predictors in the model take a new sparsity-inducing prior. The applicability of the proposed model is examined through a set of simulation studies. We apply the proposed model to predict the annual ambient particulate matter (PM (Formula presented.)) concentrations for zip code locations in Massachusetts, Connecticut and Rhode Island.