Precise knowledge of causal directed acyclic graphs (DAGs) is assumed for standard approaches towards valid adjustment set selection for unbiased estimation, but in practice, the DAG is often inferred from data or expert knowledge, introducing uncertainty. We present techniques to identify valid adjustment sets despite potential errors in the estimated causal graph. Specifically, we assume that only the skeleton of the DAG is known. Under a Bayesian framework, we place a prior on graphs and wish to sample graphs and compute the posterior probability of each set being valid; however, directly doing so is inefficient as the number of sets grows exponentially with the number of nodes in the DAG. We develop theory and techniques so that a limited number of sets are tested while the probability of finding valid adjustment sets remains high. Empirical results demonstrate the effectiveness of the method.

翻译：标准方法在选取有效调整集以进行无偏估计时，通常假设因果有向无环图（DAG）的精确知识已知，但在实践中，DAG往往是从数据或专家知识中推断得出的，这引入了不确定性。我们提出了在估计因果图可能存在错误的情况下识别有效调整集的技术。具体而言，我们假设仅已知DAG的骨架结构。在贝叶斯框架下，我们对图施加先验分布，并希望采样图并计算每个集合为有效的后验概率；然而，由于集合数量随DAG中节点数呈指数增长，直接进行此操作效率低下。我们发展了理论和相关技术，使得在测试有限数量集合的同时，仍能保持找到有效调整集的概率较高。实证结果证明了该方法的有效性。