On a dualization of graphical Gaussian models
On a dualization of graphical Gaussian models
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图解高斯模型的对偶化
DOI：
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发表时间：
1996
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通讯作者：
G. Kauermann
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作者：
G. Kauermann
由Speed & Kiiveri（1986）定义的图形高斯模型通过图形表示正态分布变量的条件独立结构。最近考克斯和韦克斯曼（1993）提出了一种类似的方法，他们引入了显示边际独立结构的图。图的条件独立关系的解释分别基于两两、局部和全局马尔可夫性质的定义，它们在正态分布中是等价的。类似的定义可以公式化的解释图的边际独立性。在正态分布中证明了它们的等价性。Frydenberg（1990 a）讨论了图形方法和指数族中的截数概念之间的等价性（Barndorff-Nielsen，1978）。在本文中，类似的关系，正态分布和图形模型的边际独立性。利用对偶似然概念实现了具有边际独立解释的图模型的参数估计，它与条件独立的图高斯模型的极大似然估计结果有着有趣的关系。
Graphical Gaussian models as defined by Speed & Kiiveri (1986) present the conditional independence structure of normally distributed variables by a graph. A similar approach was recently motivated by Cox & Wermuth (1993) who introduced graphs showing the marginal independence structure. The interpretation of a graph in terms of conditional indepen- dence relations is based on the definition of a pairwise, local and global Markov property respectively, which are equivalent in the normal distribution. Similar definitions can be formu- lated for the interpretation of graphs in terms of marginal independencies. Their equivalence is proven in the normal distribution. Frydenberg (1990a) discusses equivalence statements between the graphical approach and the concept of a cut in exponential families (Barndorff-Nielsen, 1978). In this paper, similar relations are shown for the normal distribution and graphical models for marginal independencies. Parameter estimation in graphical models with marginal indepen- dence interpretation is achieved by the dual likelihood concept, which shows interesting relations to results available for maximum likelihood estimation in graphical Gaussian models for conditional independence.