47: Extending Bayesian additive regression trees to handle non-stationary spatial data

Music City Center 

Mixed spatial effects models are widely used in the analysis of geospatial data. Such models typically consist of a mean function, which depends on covariates, and spatial random effects. Various approaches are available to model the mean structure in a non-linear way, mostly non-parametric methods such as generalized additive models (GAM) or machine learning methods. A common assumption is that the flexible mean function accounts for all the spatial dependence, thus implying that there is no residual spatial dependence and the errors can be taken as independent. Recent work has sought to relax this assumption on the errors, while still retaining the hypothesis that the spatially dependent errors are second-order stationary.
In this talk, we relax the assumption that the spatial random effects arise as realization of a stationary spatial process, and we highlight how Bayesian additive regression trees(BART) leads to systematic errors in this situation. To address this shortcoming, we propose a new BART-based approach that accommodate both stationary and nonstationary geospatial data. Namely, our proposal addresses to overly assign locations to the same leaf nodes as neighboring observations.

Random Forest

Non-stationary spatial data 

Section on Statistical Learning and Data Science