  We present a method for incorporating missing data in non-parametric
statistical learning without the need for imputation. We focus on a tree-based
method, Bayesian Additive Regression Trees (BART), enhanced with "Missingness
Incorporated in Attributes," an approach recently proposed incorporating
missingness into decision trees (Twala, 2008). This procedure takes advantage
of the partitioning mechanisms found in tree-based models. Simulations on
generated models and real data indicate that our proposed method can forecast
well on complicated missing-at-random and not-missing-at-random models as well
as models where missingness itself influences the response. Our procedure has
higher predictive performance and is more stable than competitors in many
cases. We also illustrate BART's abilities to incorporate missingness into
uncertainty intervals and to detect the influence of missingness on the model
fit.
