Independence Concepts for Convex Sets of Probabilities

In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independ­ ence. The first is irrelevance. Two variables are independent when a change on the know­ ledge about one variable does not affect the other. The second one is factorization. Two variables are independent when the joint con­ vex 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 defini­ tion. In the case of convex sets of probabil­ ities, 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.