Bayesian networks in the form of Directed Acyclic Graphs (DAGs) represent an effective tool for modeling and inferring dependence relations among variables, a process known as structural learning. In addition, when equipped with the notion of intervention, a causal DAG model can be adopted to quantify the causal effect on a response due to a hypothetical intervention on some variable. Observational data cannot distinguish between DAGs encoding the same set of conditional independencies (Markov equivalent DAGs), which however can be different from a causal perspective. In addition, because causal effects depend on the underlying network structure, uncertainty around the DAG generating model crucially affects the causal estimation results. We propose a Bayesian methodology which combines structural learning of Gaussian DAG models and inference of causal effects as arising from simultaneous interventions on any given set of variables in the system. Our approach fully accounts for the uncertainty around both the network structure and causal relationships through a joint posterior distribution over DAGs, DAG parameters and then causal effects.

有向无环图 (DAG) 形式的贝叶斯网络是建模和推断变量之间依赖关系的有效工具，这一过程称为结构学习。此外，当配备干预的概念时，可以采用因果DAG 模型来量化由于对某些变量的假设干预而对响应产生的因果影响。观测数据无法区分编码相同条件独立集（马尔可夫等效 DAG）的 DAG，但是这可能与因果关系不同看法。此外，由于因果效应取决于底层网络结构，围绕 DAG 生成模型的不确定性对因果估计结果至关重要。我们提出了一种贝叶斯方法，它结合了高斯 DAG 模型的结构学习和对系统中任何给定变量集的同时干预所产生的因果效应的推断。我们的方法通过 DAG、DAG 参数和因果效应的联合后验分布，充分考虑了网络结构和因果关系的不确定性。