Causal discovery procedures aim to deduce causal relationships among variables in a multivariate dataset. While various methods have been proposed for estimating a single causal model or a single equivalence class of models, less attention has been given to quantifying uncertainty in causal discovery in terms of confidence statements. The primary challenge in causal discovery is determining a causal ordering among the variables. Our research offers a framework for constructing confidence sets of causal orderings that the data do not rule out. Our methodology applies to structural equation models and is based on a residual bootstrap procedure to test the goodness-of-fit of causal orderings. We demonstrate the asymptotic validity of the confidence set constructed using this goodness-of-fit test and explain how the confidence set may be used to form sub/supersets of ancestral relationships as well as confidence intervals for causal effects that incorporate model uncertainty.

翻译：因果发现方法旨在推断多变量数据集中变量间的因果关系。尽管已有多种方法可估计单个因果模型或单一等价类模型，但基于置信声明来量化因果发现中的不确定性仍较少受到关注。因果发现的主要挑战在于确定变量间的因果排序。我们的研究提出了一种框架，用于构建数据无法排除的因果排序置信集。该方法适用于结构方程模型，并基于残差自助法检验因果排序的拟合优度。我们证明了通过该拟合优度检验构建的置信集具有渐近有效性，并阐释了如何利用该置信集生成祖先关系的子集/超集，以及纳入模型不确定性的因果效应置信区间。