Inductive Inference and the Representation of Uncertainty

Abstract

Publisher Summary This chapter discusses inductive inference and the representation of uncertainty. The form and justification of inductive inference rules depend strongly on the representation of uncertainty. The notion can be formalized by presuming that the relevant probabilities in a decision problem are known only to the extent that they belong to a class K of probability distributions. The concept is a generalization of a frequent suggestion that uncertainty be represented by intervals or ranges on probabilities. To make the representation useful for decision making, an inductive rule can be formulated, which determines, in a well-defined manner, a best approximation to the unknown probability, given the set K. In addition to an inference rule, a complete theory of induction requires an updating procedure, that is, a method of revising an estimate given new evidence. In effect, this entails a method of modifying the knowledge set K based on the new evidence, as the revised estimate can then be obtained by applying the min-score rule to the new K.