The Bayesian additive regression trees (BART) model is an ensemble method extensively and successfully used in regression tasks due to its consistently strong predictive performance and its ability to quantify uncertainty. BART combines "weak" tree models through a set of shrinkage priors, whereby each tree explains a small portion of the variability in the data. However, the lack of smoothness and the absence of an explicit covariance structure over the observations in standard BART can yield poor performance in cases where such assumptions would be necessary. The Gaussian processes Bayesian additive regression trees (GP-BART) model is an extension of BART which addresses this limitation by assuming Gaussian process (GP) priors for the predictions of each terminal node among all trees. The model's effectiveness is demonstrated through applications to simulated and real-world data, surpassing the performance of traditional modeling approaches in various scenarios.

翻译：贝叶斯加性回归树（BART）模型是一种集成方法，因其在回归任务中始终表现出强劲的预测性能以及具有量化不确定性的能力而被广泛且成功地使用。BART通过一组收缩先验将“弱”树模型组合起来，其中每棵树解释数据中一小部分变异性。然而，标准BART缺乏平滑性，并且观测值之间没有显式的协方差结构，在需要这些假设的情形下可能导致性能不佳。高斯过程贝叶斯加性回归树（GP-BART）模型是BART的一种扩展，它通过为所有树中每个终节点的预测假设高斯过程（GP）先验来解决这一局限性。该模型的有效性通过模拟和真实数据应用得到证明，在各种场景中均超越了传统建模方法的性能。