局部独立图的非对称分离
Asymmetric separation for local independence graphs
摘要：
Didelez（2000）和Nodelmann et al.（2002）提出了有向可能循环图来表示随机过程之间的动态依赖关系。这些依赖性是基于Granger因果关系到连续时间的推广，首先由Schweder（1970）为马尔可夫过程开发的，他称之为局部依赖性。它们值得特别关注，因为它们不对称，不像随机（不）依赖。在本文中，我们专注于他们的图形表示和开发一个合适的，即不对称的概念分离，称为三角洲分离。这种图形分离以及局部独立的属性进行了详细研究的框架内的非对称（半）graphoid允许更深入地了解什么信息可以读取这些图。
英文摘要：
Directed possibly cyclic graphs have been proposed by Didelez (2000) and Nodelmann et al. (2002) in order to represent the dynamic dependencies among stochastic processes. These dependencies are based on a generalization of Granger-causality to continuous time, first developed by Schweder (1970) for Markov processes, who called them local dependencies. They deserve special attention as they are asymmetric unlike stochastic (in)dependence. In this paper we focus on their graphical representation and develop a suitable, i.e. asymmetric notion of separation, called delta-separation. The properties of this graph separation as well as of local independence are investigated in detail within a framework of asymmetric (semi)graphoids allowing a deeper insight into what information can be read off these graphs.
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