Robust Regression in Environmental Modeling Based on Bayesian Additive Regression Trees

One challenging task in analyzing environmental data is how to achieve better prediction in presence of outliers, which is inevitable, especially in environmental modeling. The purpose of prediction is to draw valid conclusions and provide useful advices in environmental management. Robust approach is often desirable when there exist outliers. Robust nonparametric regression methods have attracted much attention from a practical point of view. As a nonparametric Bayesian approach, Bayesian additive regression trees (BART) provides a flexible regression that captures potential nonlinear relationships and complex interactions via the framework including sum-of-trees model, regularization prior and Bayesian backfitting MCMC algorithm (hereafter backfitting MCMC). When outliers are present in the data, we find out that BART has the highest prediction performance in simulation studies which are carried out in a variety of cases, compared to the well-known machine learning methods: random forest, support vector machine, extreme gradient boosting. The findings of this study demonstrate that BART approach is seen to be remarkably robust to outliers. For illustration, we also analyze two datasets which exist many underlying outliers: one from a study of forest fires related factors and the other from a study of biomass fuels.