Prediction with missing data via Bayesian Additive Regression Trees

We present a method for incorporating missing data into general prediction problems which use nonparametric statistical learning. We focus on a tree‐based method, Bayesian Additive Regression Trees ( BART ), enhanced with “Missingness Incorporated in Attributes,” a recently proposed approach for incorporating missingness into decision trees. This procedure extends the native partitioning mechanisms found in tree‐based models and does not require imputation. Simulations on generated models and real data indicate that our procedure offers promise for both selection model and pattern‐mixture frameworks as measured by out‐of‐sample predictive accuracy. We also illustrate BART 's abilities to incorporate missingness into uncertainty intervals. Our implementation is readily available in the R package bartMachine . The Canadian Journal of Statistics 43: 224–239; 2015 © 2015 Statistical Society of Canada