For questions regarding imprecise probability, which concerns concepts and methods generalizing probability theory beyond real-valued probability measures. It includes extensions of Bayesian methods to reflect uncertainty in degrees of confidence, and covers among other things, upper and lower previsions, interval-valued probability, credal sets, lower envelopes, and Choquet capacities.
Imprecise probabilities are a natural and intuitive way of overcoming some of the issues with orthodox precise probabilities. Models of this type have a long pedigree, and interest in such models has been growing in recent years.
Imprecise probability can be looked as a generalization of the traditional probability to allow for partial probability specifications, and is applicable when information is scarce, vague, or conflicting, in which case a unique probability distribution may be hard to identify.
For example, instead of a precise value of the probabilistic measure $~\text{Pr}(A)=p~$ associated with an event $~A~,$ a pair of lower and upper probabilities $~\text{Pr}(A)=[p_1,~p_2]~$ could be used to include a set of probabilities and quantify the aleatory and epistemic uncertainties simultaneously. The range of the interval $~[p_1,~p_2]~$ captures the epistemic uncertainty component. There are also some applications of imprecise probability to objective probabilities associated with frequencies, for example.
Closely related terms include include "indeterminate probability" and "hyper-randomness".
For more details you may follow the following references:
Introduction to Imprecise Probabilities edited by Thomas Augustin, Frank P. A. Coolen, Gert de Cooman, Matthias C. M. Troffaes
Towards a unified theory of imprecise probability by Peter Walley
Imprecise Probability by Frank P. A. Coolen, Matthias C. M. Troffaes, Thomas Augustin
Imprecise Probability as an Approach to Improved Dependability in High-Level Information Fusion by Alexander Karlsson, Ronnie Johansson, Sten F. Andler
Imprecise Probabilities by Seamus Bradley in the Stanford Encyclopedia of Philosophy
FAQs of Imprecise Probability
