  We propose a simple yet powerful extension of Bayesian Additive Regression
Trees which we name Hierarchical Embedded BART (HE-BART). The model allows for
random effects to be included at the terminal node level of a set of regression
trees, making HE-BART a non-parametric alternative to mixed effects models
which avoids the need for the user to specify the structure of the random
effects in the model, whilst maintaining the prediction and uncertainty
calibration properties of standard BART. Using simulated and real-world
examples, we demonstrate that this new extension yields superior predictions
for many of the standard mixed effects models' example data sets, and yet still
provides consistent estimates of the random effect variances. In a future
version of this paper, we outline its use in larger, more advanced data sets
and structures.
