摘要翻译：
在图形建模中，双向图对随机变量之间的边缘独立性进行编码，这些随机变量与图的顶点是一致的。给出了如何将一个双向有向图转换成一个与原双向有向图具有相同独立结构的极大祖先图，并使满足(i)的所有祖先图中的箭头数最小化。这里，祖先图的箭头数是有向边数加上双有向边数的两倍。在高斯模型中，这种构造可以用于更有效地迭代最大似然函数，并确定最大似然估计何时等于经验对应项。
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英文标题：
《Graphical methods for efficient likelihood inference in Gaussian
  covariance models》
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作者：
Mathias Drton, Thomas S. Richardson
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  In graphical modelling, a bi-directed graph encodes marginal independences among random variables that are identified with the vertices of the graph. We show how to transform a bi-directed graph into a maximal ancestral graph that (i) represents the same independence structure as the original bi-directed graph, and (ii) minimizes the number of arrowheads among all ancestral graphs satisfying (i). Here the number of arrowheads of an ancestral graph is the number of directed edges plus twice the number of bi-directed edges. In Gaussian models, this construction can be used for more efficient iterative maximization of the likelihood function and to determine when maximum likelihood estimates are equal to empirical counterparts.
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PDF链接：
https://arxiv.org/pdf/708.1321