A Posteriori Representations Based on Linear Inequality Descriptions of a Priori and Conditional Probabilities

Abstract
Two simple generalizations of Bayes' rule are presented that 1) allow both a priori probabilities and conditional probabilities to be described by linear inequalities and 2) produce an extreme point description and a linear inequality description of a set containing all possible a posteriori probabilities. Linear inequalities to describe a priori and conditional probabilities are used since many natural language statements that describe ambiguity, unpredictability, or randomness can be adequately modeled by such constraints. The perceived potential usefulness of these results is to support inference mechanisms in knowledge systems.