MVR 链图属性 (On the Properties of MVR Chain Graphs)

Depending on the interpretation of the type of edges, a chain graph can represent different relations between variables and thereby independence models. Three interpretations, known by the acronyms LWF, MVR, and AMP, are prevalent. Multivariate regression (MVR) chain graphs were introduced by Cox and Wermuth in 1993. We review Markov properties for MVR chain graphs and propose an alternative global and local Markov property for them. Also, we prove equivalence of all proposed Markov properties in the literature for compositional graphoids. We derive a new factorization formula for MVR chain graphs which is more explicit than and different from the proposed factorizations for MVR chain graphs in the literature. Finally, we provide a summary table comparing different features of LWF, AMP, and MVR chain graphs.

翻译：视对边缘类型的解释而定,链条图可以代表不同变量和独立模型之间的不同关系。三种解释(缩略语LWF、MVR和AMP)很普遍。1993年Cox和Wermuth采用了多变回归链图。我们审查了MVR链图的Markov属性,并为它们提出了一个替代的全球和地方Markov属性。此外,我们还证明,在成文图的文献中,所有拟议的Markov属性都与成文图相等。我们为MVR链图提出了一个新的因子化公式,该公式比文献中MVR链图的拟议因子化更清楚,也不同。最后,我们提供了一个总表,比较LWFF、AMP和MVR链图的不同特征。