论文标题
通过马尔可夫树对多元极值分布进行建模
Modelling multivariate extreme value distributions via Markov trees
论文作者
论文摘要
多元极端价值分布是建模多元极端的常见选择。但是，在高维度中，灵活和简约的模型的构建具有挑战性。我们建议将双变量最大分布组合到马尔可夫随机场上相对于树。尽管通常不是最大稳定本身，但该马尔可夫树被多元最大稳定分布所吸引。后者用作基于树的最大分布的基于树的近似值，并作为边缘作为边缘的给定双变量分布。给定数据，我们通过PRIM的算法学习了适当的树结构，其估计的成对上尾依赖系数是边缘重量。可以以各种方式拟合连接变量对的分布。所得树结构的最大分布可以推断出稀有事件概率，如上多瑙河上部的河流排放数据所示。
Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max-stable distributions into a Markov random field with respect to a tree. Although in general not max-stable itself, this Markov tree is attracted by a multivariate max-stable distribution. The latter serves as a tree-based approximation to an unknown max-stable distribution with the given bivariate distributions as margins. Given data, we learn an appropriate tree structure by Prim's algorithm with estimated pairwise upper tail dependence coefficients as edge weights. The distributions of pairs of connected variables can be fitted in various ways. The resulting tree-structured max-stable distribution allows for inference on rare event probabilities, as illustrated on river discharge data from the upper Danube basin.
