标题： 藤 copula 结构的矩阵和图表示 显示英文标题

标题： Matrix and graph representations of vine copula structures

摘要： 藤copula 可以有效地建模多变量概率分布。 本文的重点是对它们的结构有更深入的理解，因为在文献中，藤copula 表示常常是模糊的。 图表示包括原始图、樱桃图和弦图序列结构，我们证明了它们之间的等价性。 重要的是，我们还展示了一个新的结果，即当给出藤结构的完美消去顺序时，则它总能唯一地用矩阵来表示。 O. M. Nápoles 展示了一种用矩阵表示藤的方法，我们将这种方法算法化，同时通过樱桃树序列展示了一种构造此类矩阵的新方法。 我们还计算了这些算法的运行时间。 最后，我们证明了如果使用相同的完美消去顺序，这两种构建矩阵的算法是等价的。 显示英文摘要

摘要： 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. N\'apoles 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.