We assume that multivariate observational data are generated from a distribution whose conditional independencies are encoded in a Directed Acyclic Graph (DAG). For any given DAG, the causal effect of a variable onto another one can be evaluated through intervention calculus. A DAG is typically not identifiable from observational data alone. However its Markov equivalence class (a collection of DAGs) can be estimated from the data. As a consequence, for the same intervention a set of causal effects, one for each DAG in the equivalence class, can be evaluated. In this paper we propose a fully Bayesian methodology to make inference on the causal effects of any intervention in the system. Main features of our method are: i) both uncertainty on the equivalence class and the causal effects are jointly modeled; ii) priors on the parameters of the modified Cholesky decomposition of the precision matrices across all DAG models are constructively assigned starting from a unique prior on the complete (unrestricted) DAG; iii) an efficient algorithm to sample from the posterior distribution on graph space is adopted; iv) an objective Bayes approach, requiring virtually no user specification, is used throughout. We demonstrate the merits of our methodology in simulation studies, wherein comparisons with current state-of-the-art procedures turn out to be highly satisfactory. Finally we examine a real data set of gene expressions for Arabidopsis thaliana. This article is protected by copyright. All rights reserved.

中文翻译：

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高斯图形模型中观察数据的因果效应的贝叶斯推断

我们假设多变量观测数据是从条件独立性编码在有向无环图 (DAG) 中的分布中生成的。对于任何给定的 DAG，可以通过干预演算来评估一个变量对另一个变量的因果影响。DAG 通常不能仅从观察数据中识别。然而，它的马尔可夫等价类（DAG 的集合）可以从数据中估计出来。因此，对于相同的干预，可以评估一组因果效应，对等类中的每个 DAG 都有一个因果效应。在本文中，我们提出了一种完全贝叶斯方法来推断系统中任何干预的因果效应。我们方法的主要特点是：i）等价类的不确定性和因果效应是联合建模的；ii) 所有 DAG 模型的精度矩阵的修正 Cholesky 分解的参数的先验是从完整（不受限制的）DAG 上的唯一先验开始建设性地分配的；iii) 采用了一种从图空间上的后验分布中采样的有效算法；iv) 一种客观的贝叶斯方法，几乎​​不需要用户指定，贯穿始终。我们证明了我们的方法在模拟研究中的优点，其中与当前最先进的程序的比较结果非常令人满意。最后，我们检查了拟南芥基因表达的真实数据集。本文受版权保护。版权所有。