Interval Probability on Finite Sample Spaces

Abstract

In the seventies and early eighties theory of interval probability has gained very much from contributions of Peter Huber. The present article gives an outline of an approach aiming to establish unifying foundations of that theory. A system of axioms for interval probability is described generalizing Kolmogorov’s axioms for classical probability and distinguishing two types of interval probability. The first one (R-probability) is characterized by employing interval-limits which are not self-contradictory, while the interval-limits of the second (F-probability) fit exactly to the set of classical probabilities in accordance to these interval-limits (structure). The task of controlling whether an assignment of intervals to each random event of a finite sample space represents at least R-probability or even F-probability is done by means of Linear Programming. The possibility of characterizing R-probability by features of its structure is sketched. A thorough presentation of theory will be given in a forthcoming book by the author.