Towards a Unified Theory of Imprecise Probability

Belief functions, possibility measures and Choquet capacities of order 2, which are special kinds of coherent upper or lower probability, are amongst the most popular mathematical models for uncertainty and partial ignorance. I give examples to show that these models are not sufficiently general to represent some common types of uncertainty. Coherent lower previsions and sets of probability measures are considerably more general but they may not be sufficiently informative for some purposes. I discuss two other models for uncertainty, involving sets of desirable gambles and partial preference orderings. These are more informative and more general than the previous models, and they may provide a suitable mathematical setting for a unified theory of imprecise probability. Keywords. Choquet capacity, coherence, comparative probability, desirable gambles, imprecise probability, incomplete preference, lower prevision, lower probability.

• Type: Conference
• Year: 1999
• Where: ISIPTA
• Authors: Peter Walley
• Keywords: Desirable Gambles, ISIPTA 1999, Lower Prevision, Lower Probability, Mathematics