Towards a unified theory of imprecise probability

✍ Scribed by Peter Walley

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 173 KB
• Volume: 24
• Category: Article
• ISSN: 0888-613X
• DOI: 10.1016/s0888-613x(00)00031-1

✦ Synopsis

Coherent upper and lower probabilities, Choquet capacities of order 2, belief functions and possibility measures are amongst the most popular mathematical models for uncertainty and partial ignorance. Examples are given to show that these models are not suciently general to represent some common types of uncertainty. In particular, they are not suciently informative about expectations and conditional probabilities. Coherent lower previsions and sets of probability measures are considerably more general, but they may not be suciently informative for some purposes. Two other models for uncertainty, which involve partial preference orderings and sets of desirable gambles, are discussed. These are more informative and more general than the previous models, and they may provide a suitable mathematical foundation for a uni®ed theory of imprecise probability.