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.

翻译：我们提出了一种简单而强大的贝叶斯加性回归树扩展方法，命名为层级嵌入式贝叶斯加性回归树（HE-BART）。该模型允许在回归树集合的叶节点层级纳入随机效应，使HE-BART成为混合效应模型的非参数替代方案。它无需用户指定模型中随机效应的结构，同时保留了标准BART的预测能力和不确定性校准特性。通过模拟和真实数据实例，我们证明了这种新扩展方法在多数标准混合效应模型示例数据集上能产生更优的预测结果，并且仍能提供随机效应方差的一致估计。在本文的未来版本中，我们将概述其在更大规模、更复杂的数据集及结构中的应用。