Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in treatment effect estimation to support decision-making in a relatively small sample size setting. Our proposed model places Gaussian process priors on the nonparametric components of a semiparametric model called a partially linear model. This model formulation has three advantages. First, we can analytically compute the posterior distribution of a treatment effect without relying on the computationally demanding posterior approximation. Second, we can guarantee that the posterior distribution concentrates around the true one as the sample size goes to infinity. Third, we can incorporate prior knowledge about a treatment effect into the prior distribution, improving the estimation efficiency. Our experimental results show that even in the small sample size setting, our method can accurately estimate the heterogeneous treatment effects and effectively quantify its estimation uncertainty.

翻译：估计个体间的异质性处理效应作为关键决策制定的统计工具已引起日益关注。我们提出一个贝叶斯推断框架，用于量化处理效应估计中的不确定性，以支持相对小样本量设定下的决策制定。所提出的模型在半参数模型（称为部分线性模型）的非参数成分上放置高斯过程先验。该模型形式具有三个优势：首先，我们能够分析计算处理效应的后验分布，而无需依赖计算密集的后验近似；其次，我们能够保证随着样本量趋于无穷大，后验分布收敛于真实分布；第三，我们能够将关于处理效应的先验知识纳入先验分布中，从而提高估计效率。实验结果表明，即使在小样本量设定下，我们的方法也能准确估计异质性处理效应并有效量化其估计不确定性。