标题： 关于与无环有向混合图相关的统计和因果模型 显示英文标题

标题： On statistical and causal models associated with acyclic directed mixed graphs

摘要： 在统计学中，因果模型通常使用无环有向混合图（ADMG）来描述，这些图包含有向边和双向边，并且没有有向环。 本文综述了ADMG的各种解释，讨论了不同子类ADMG之间的关系，并认为其中一种解释——噪声扩展（NE）模型——应作为默认解释。 我们支持NE模型是基于两个观察结果。 首先，在称为无混杂图的ADMG子类中（保留了大部分有向无环图和双向图的良好性质），NE模型等价于许多其他解释，包括全局马尔可夫和嵌套马尔可夫模型。 其次，任意ADMG的NE模型恰好是该图所有无混杂扩展的NE模型的并集。 这一特性被称为完备性，因为它表明该模型不承诺任何特定的潜在变量解释。 在证明NE模型是嵌套马尔可夫的过程中，我们还开发了一种基于ADMG的因果理论。 最后，我们将NE模型与ADMG作为带有潜在变量的有向无环图（DAG）的密切相关但不同的解释进行了比较，这种解释在文献中很常见。 我们认为“潜在DAG”解释在数学上是不必要的，会带来模糊的本体论假设，并鼓励从业者不去仔细考虑重要的结构假设。 显示英文摘要

摘要： Causal models in statistics are often described using acyclic directed mixed graphs (ADMGs), which contain directed and bidirected edges and no directed cycles. This article surveys various interpretations of ADMGs, discusses their relations in different sub-classes of ADMGs, and argues that one of them -- the noise expansion (NE) model -- should be used as the default interpretation. Our endorsement of the NE model is based on two observations. First, in a subclass of ADMGs called unconfounded graphs (which retain most of the good properties of directed acyclic graphs and bidirected graphs), the NE model is equivalent to many other interpretations including the global Markov and nested Markov models. Second, the NE model for an arbitrary ADMG is exactly the union of that for all unconfounded expansions of that graph. This property is referred to as completeness, as it shows that the model does not commit to any specific latent variable explanation. In proving that the NE model is nested Markov, we also develop an ADMG-based theory for causality. Finally, we compare the NE model with the closely related but different interpretation of ADMGs as directed acyclic graphs (DAGs) with latent variables that is commonly used in the literature. We argue that the "latent DAG" interpretation is mathematically unnecessary, makes obscure ontological assumptions, and discourages practitioners from deliberating over important structural assumptions.