A definition of conditional probability distribution with non-stochastic information

Abstract

The current definition of a conditional probability distribution enables one to update probabilities only on the basis of stochastic information. This paper provides a definition for conditional probability distributions with non-stochastic information. The definition is derived as a solution of a decision theoretic problem, where the information is connected to the outcome of interest via a loss function. We shall show that the Kullback-Leibler divergence plays a central role. Some illustrations are presented.