论文标题
葡萄藤结构的基质和图表
Matrix and graph representations of vine copula structures
论文作者
论文摘要
葡萄藤可以有效地对多元概率分布进行建模。本文着重于对其结构的更透彻的理解，因为在文献中，藤蔓的表征通常是模棱两可的。图表包括原始，樱桃和和弦图序列结构，我们在两者之间表现出等效性。重要的是，我们还展示了一个新的结果，即，当给出葡萄结构的完美消除订购时，它始终可以用矩阵唯一地表示。 O. M.Nápoles已显示出一种表示矩阵中葡萄藤的方法，并且我们算法对以前的方法进行算法，同时还通过樱桃树序列显示了一种新的方法来构建此类矩阵。我们还计算这些算法的运行时。最后，我们证明，如果使用相同的完美消除顺序，这两个矩阵构建算法是等效的。
Vine copulas can efficiently model multivariate probability distributions. This paper focuses on a more thorough understanding of their structures, since in the literature, vine copula representations are often ambiguous. The graph representations include the original, cherry and chordal graph sequence structures, which we show equivalence between. Importantly we also show a new result, namely that when a perfect elimination ordering of a vine structure is given, then it can always be uniquely represented with a matrix. O. M. Nápoles has shown a way to represent vines in a matrix, and we algorithmify this previous approach, while also showing a new method for constructing such a matrix, through cherry tree sequences. We also calculate the runtime of these algorithms. Lastly, we prove that these two matrix-building algorithms are equivalent if the same perfect elimination ordering is being used.
