混合图的马尔可夫性
Markov properties for mixed graphs
摘要：
本文通过引入无环混合图类，统一了用于图马尔可夫模型的各种不同类型图的马尔可夫理论，并证明了在这类图上由$m$ -分离导出的所有独立模型都是合成图胚.我们特别关注无带图的子类，作为特殊情况，包括无向图，双向图，有向无环图，以及祖先图和摘要图。我们定义了这类图的极大性以及一个两两和一个全局马尔可夫性。我们证明了一个极大无带图的全局和两两马尔可夫性对于任何独立的组合图面模型都是等价的。
英文摘要：
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such graphs are compositional graphoids. We focus in particular on the subclass of ribbonless graphs which as special cases include undirected graphs, bidirected graphs, and directed acyclic graphs, as well as ancestral graphs and summary graphs. We define maximality of such graphs as well as a pairwise and a global Markov property. We prove that the global and pairwise Markov properties of a maximal ribbonless graph are equivalent for any independence model that is a compositional graphoid.
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