We introduce a framework for estimating causal effects of binary and continuous treatments in high dimensions. We show how posterior distributions of treatment and outcome models can be used together with doubly robust estimators. We propose an approach to uncertainty quantification for the doubly robust estimator, which utilizes posterior distributions of model parameters and (1) results in good frequentist properties in small samples, (2) is based on a single run of a Markov chain Monte Carlo (MCMC) algorithm, and (3) improves over frequentist measures of uncertainty which rely on asymptotic properties. We consider a flexible framework for modeling the treatment and outcome processes within the Bayesian paradigm that reduces model dependence, accommodates nonlinearity, and achieves dimension reduction of the covariate space. We illustrate the ability of the proposed approach to flexibly estimate causal effects in high dimensions and appropriately quantify uncertainty. We show that our proposed variance estimation strategy is consistent when both models are correctly specified, and we see empirically that it performs well in finite samples and under model misspecification. Finally, we estimate the effect of continuous environmental exposures on cholesterol and triglyceride levels.

中文翻译：

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高维度的因果推理：贝叶斯建模与良好的常客属性之间的结合

我们引入了一个框架，用于在高维度上估计二元和连续处理的因果效应。我们展示了如何将治疗和结果模型的后验分布与双重稳健的估计量一起使用。我们提出了一种双重鲁棒估计器的不确定性量化方法，该方法利用模型参数的后验分布，并且（1）在小样本中产生良好的频率特性，（2）基于马尔可夫链蒙特卡罗（MCMC）的单次运行) 算法，以及 (3) 改进了依赖于渐近特性的不确定性的频繁测量。我们考虑了一个灵活的框架，用于在贝叶斯范式中对治疗和结果过程进行建模，以减少模型依赖性、适应非线性并实现协变量空间的降维。我们说明了所提出的方法能够灵活地估计高维因果效应并适当量化不确定性。我们表明，当两个模型都正确指定时，我们提出的方差估计策略是一致的，并且我们凭经验看到它在有限样本和模型错误指定的情况下表现良好。最后，我们估计了持续环境暴露对胆固醇和甘油三酯水平的影响。