Bayesian Causal Forests (BCF) is a causal inference machine learning model based on a highly flexible non-parametric regression and classification tool called Bayesian Additive Regression Trees (BART). Motivated by data from the Trends in International Mathematics and Science Study (TIMSS), which includes data on student achievement in both mathematics and science, we present a multivariate extension of the BCF algorithm. With the help of simulation studies we show that our approach can accurately estimate causal effects for multiple outcomes subject to the same treatment. We also apply our model to Irish data from TIMSS 2019. Our findings reveal the positive effects of having access to a study desk at home (Mathematics ATE 95% CI: [0.20, 11.67]) while also highlighting the negative consequences of students often feeling hungry at school (Mathematics ATE 95% CI: [-11.15, -2.78] , Science ATE 95% CI: [-10.82,-1.72]) or often being absent (Mathematics ATE 95% CI: [-12.47, -1.55]).

翻译：贝叶斯因果森林（BCF）是一种基于高度灵活的非参数回归与分类工具——贝叶斯加性回归树（BART）的因果推断机器学习模型。受国际数学与科学趋势研究（TIMSS）中涵盖学生数学与科学成绩数据的启发，我们提出了BCF算法的多变量扩展。通过模拟研究，我们证明该方法能够准确估计同一处理对多个结局的因果效应。我们还将该模型应用于TIMSS 2019的爱尔兰数据。研究结果揭示了家庭学习桌配备的积极效应（数学ATE 95% CI：[0.20, 11.67]），同时强调了学生在校频繁感到饥饿（数学ATE 95% CI：[-11.15, -2.78]；科学ATE 95% CI：[-10.82,-1.72]）或频繁缺课（数学ATE 95% CI：[-12.47, -1.55]）所带来的负面影响。