论文标题
$ p $盒的普通锥和极端点的完整表征
A complete characterization of normal cones and extreme points for $p$-boxes
论文作者
论文摘要
概率框，也称为$ p $盒，对应于由一对分布函数界定的概率分布集。它们属于称为不精确概率的模型类别。与不精确概率相关的中心问题之一是值的间隔，与随机变量的期望相对应，尤其是间隔边界。通常，在信用集的极端点上获得这些，这表示兼容概率模型的凸集。本文的目的是对对应于有限域上$ p $盒的极端点的表征和识别。为此，我们利用了普通锥的概念。在不精确概率的设置中，那些对应于一组随机变量的集合，这些变量的极端期望是在一个共同的极端点上达到的。我们的主要结果包括表征$ p $盒的所有可能的正常锥体，它们与极端点的关系以及在收集正常锥体上的邻接结构的识别，与极端点集中的邻接结构密切相关。
Probability boxes, also known as $p$-boxes, correspond to sets of probability distributions bounded by a pair of distribution functions. They fall into the class of models known as imprecise probabilities. One of the central questions related to imprecise probabilities are the intervals of values corresponding to expectations of random variables, and especially the interval bounds. In general, those are attained in extremal points of credal sets, which denote convex sets of compatible probabilistic models. The aim of this paper is a characterization and identification of extreme points corresponding to $p$-boxes on finite domains. To accomplish this, we utilize the concept of normal cones. In the settings of imprecise probabilities, those correspond to sets of random variables whose extremal expectations are attained in a common extreme point. Our main results include a characterization all possible normal cones of $p$-boxes, their relation with extreme points, and the identification of adjacency structure on the collection of normal cones, closely related to the adjacency structure in the set of extreme points.
