Imprecise probability is a generalization of the classical probability theory that allows for the representation of uncertainty in situations where precise probabilities are not available or not suitable. The concept is useful for modeling and reasoning with incomplete or ambiguous information. Imprecise probability encompasses various formalisms, such as credal sets, lower previsions, and belief functions, among others.
Imprecise probability can be formalized in different ways,some of which include
Credal Sets: A credal set is a closed convex set of probability distributions, representing a range of possible distributions that may accurately represent an agent’s uncertainty. Credal sets were introduced by Levi (1980) and further developed by Walley (1991). Most other formalizations of imprecise probability can be seen as special cases of credal sets embbed naturally in them.
Belief Functions: Belief functions, also known as Dempster-Shafer theory or evidence theory, are a generalization of probability theory that allows for representing partial beliefs. They are based on the concept of mass functions, which assign a weight to each subset of a finite set of alternatives, subject to certain consistency conditions.
Walley, P. (1991). Statistical reasoning with imprecise probabilities. London: Chapman and Hall.
Augustin, T., Coolen, F., de Cooman, G., & Troffaes, M. C. M. (2014). Introduction to imprecise probabilities. Wiley.
Levi, I. (1980). The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance. MIT Press.
Shafer, G. (1976). A Mathematical Theory of Evidence. Princeton University Press.
Created on May 4, 2023 at 16:21:10. See the history of this page for a list of all contributions to it.