Epistemic independence for imprecise probabilities

AbstractThe aim of this paper is that of studying a notion of independence for imprecise probabilities which is essentially based on the intuitive meaning of this concept. This is expressed, in the case of two events, by the reciprocal irrelevance of the knowledge of the value of each event for evaluating the other one, and has been termed epistemic independence. In order to consider more general situations in the framework of coherent imprecise probabilities, a definition of (epistemic) independence is introduced referring to arbitrary sets of logically independent partitions. Logical independence is viewed as a natural prerequisite for epistemic independence. It is then proved that the definition is always consistent, its relationship with the factorization rule is analysed, and some of its more relevant implications are discussed