Towards a unified theory of imprecise probability

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 mea...

Imprecise probability trees: Bridging two theories of imprecise probability

We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley’s behavioural theory of imprecise probabilities, and Shafer and Vovk’s game-theoretic account of probability. We show that the two theories are more closely related than would be suspected at first sight, and we establish a correspondence between them that...

Imprecise Probability

Imprecise Probability

1 Overview Quantification of uncertainty is mostly done by the use of precise probabilities: for each event A, a single (classical, precise) probability P (A) is used, typically satisfying Kolmogorov's axioms [4]. Whilst this has been very successful in many applications, it has long been recognized to have severe limitations. Classical probability requires a very high level of precision and co...

Towards a Unified Theory of Timed Automata

Title of dissertation: TOWARDS A UNIFIED THEORY OF TIMED AUTOMATA Peter Christopher Fontana, Doctor of Philosophy, 2014 Dissertation directed by: Professor Rance Cleaveland Department of Computer Science Timed automata are finite-state machines augmented with special clock variables that reflect the advancement of time. Able to both capture real-time behavior and be verified algorithmically (mo...