Regression discontinuity designs (RDD) are widely used for causal inference. In many empirical applications, treatment effects vary substantially with covariates, and ignoring such heterogeneity can lead to misleading conclusions, which motivates flexible modeling of heterogeneous treatment effects in RDD. To this end, we propose a Bayesian nonparametric approach to estimating heterogeneous treatment effects based on Bayesian Additive Regression Trees (BART). The key feature of our method lies in adopting a general Bayesian framework using a pseudo-model defined through a loss function for fitting local linear models around the cutoff, which gives direct modeling of heterogeneous treatment effects by BART. Optimal selection of the bandwidth parameter for the local model is implemented using the Hyvärinen score. Through numerical experiments, we demonstrate that the proposed approach flexibly captures complicated structures of heterogeneous treatment effects as a function of covariates.

翻译：断点回归设计（RDD）被广泛应用于因果推断。在许多实证应用中，处理效应随协变量显著变化，忽略这种异质性可能导致误导性结论，这促使了在RDD中对异质性处理效应进行灵活建模的需求。为此，我们提出了一种基于贝叶斯加性回归树（BART）的贝叶斯非参数方法来估计异质性处理效应。我们方法的核心特点在于采用一个通用贝叶斯框架，通过一个由损失函数定义的伪模型来拟合断点附近的局部线性模型，从而实现了通过BART直接对异质性处理效应进行建模。局部模型的带宽参数使用Hyvärinen评分进行优化选择。通过数值实验，我们证明了所提出的方法能够灵活地捕捉作为协变量函数的异质性处理效应的复杂结构。