Much of the causal discovery literature prioritises guaranteeing the identifiability of causal direction in statistical models. For structures within a Markov equivalence class, this requires strong assumptions which may not hold in real-world datasets, ultimately limiting the usability of these methods. Building on previous attempts, we show how to incorporate causal assumptions within the Bayesian framework. Identifying causal direction then becomes a Bayesian model selection problem. This enables us to construct models with realistic assumptions, and consequently allows for the differentiation between Markov equivalent causal structures. We analyse why Bayesian model selection works in situations where methods based on maximum likelihood fail. To demonstrate our approach, we construct a Bayesian non-parametric model that can flexibly model the joint distribution. We then outperform previous methods on a wide range of benchmark datasets with varying data generating assumptions.

翻译：因果发现领域的诸多研究侧重于保证统计模型中因果方向的可识别性。对于马尔可夫等价类中的结构，这需要依赖在现实数据集中可能不成立的强假设，最终限制了这些方法的实用性。基于先前的研究尝试，我们展示了如何在贝叶斯框架内整合因果假设。因果方向的识别由此转化为贝叶斯模型选择问题。这使我们能够构建具有现实性假设的模型，从而得以区分马尔可夫等价的因果结构。我们分析了贝叶斯模型选择在基于最大似然的方法失效的场景中为何有效。为验证本方法，我们构建了一个能够灵活建模联合分布的贝叶斯非参数模型。随后在涵盖不同数据生成假设的多种基准数据集上，我们的方法超越了先前所有方法。