概率凸集的独立性概念
Independence Concepts for Convex Sets of Probabilities
摘要：
本文研究了概率凸集的独立性的不同概念。对于独立性有两个基本的想法。第一个是无关性。当一个变量的知识变化不影响另一个变量时，两个变量是独立的。第二个是因式分解。当概率的联合凸集可分解为边缘凸集的乘积时，两个变量是独立的。在概率论的情况下，这两个出发点产生了相同的定义。在概率的凸集的情况下，所得到的概念将是强相关的，但它们不会是等价的。作为独立性概念的应用，我们将考虑从概率的边缘凸集构造全局凸集的问题。
英文摘要：
In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independence. The first is irrelevance. Two variables are independent when a change on the knowledge about one variable does not affect the other. The second one is factorization. Two variables are independent when the joint convex set of probabilities can be decomposed on the product of marginal convex sets. In the case of the Theory of Probability, these two starting points give rise to the same definition. In the case of convex sets of probabilities, the resulting concepts will be strongly related, but they will not be equivalent. As application of the concept of independence, we shall consider the problem of building a global convex set from marginal convex sets of probabilities.
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