LWF链图的边化与条件化
Marginalization and Conditioning for LWF Chain Graphs
摘要：
本文利用LWF马尔可夫性研究了链图节点集的两个不相交子集的边缘化和条件化问题。为此，我们定义了一类链混合图（CMG）与三种类型的边缘，并为这个类，提供了一个分离标准下，一类CMG是稳定的边缘化和条件，并包含类的LWF CG作为其子类。我们提供了一种方法，用于生成这样的图形边缘化和条件后，为一个给定的CMG或给定的LWF CG。然后，我们定义和研究类的前图，这也是稳定的边缘化和条件，并包含LWF CG，但有一个简单的结构比CMG。
英文摘要：
In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain mixed graphs (CMGs) with three types of edges and, for this class, provide a separation criterion under which the class of CMGs is stable under marginalization and conditioning and contains the class of LWF CGs as its subclass. We provide a method for generating such graphs after marginalization and conditioning for a given CMG or a given LWF CG. We then define and study the class of anterial graphs, which is also stable under marginalization and conditioning and contains LWF CGs, but has a simpler structure than CMGs.
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