Lower probability models for uncertainty and non-deterministic processes
This paper contains an excellent review of the major non-standard models of uncertainty, and concludes that the set of lower envelopes represents a useful formalism that includes classical probabilities, as well as the theory of belief functions [cf. \textit{G. Shafer}, A mathematical theory of evidence. (1976; Zbl 0359.62002)]. The reviewers work, Probability and the logic of rational belief, Wesleyan University Press (1961), might have been cited among the early works considering lower probabilities. There are advantages to this model in formalizing the aggregation of opinions or in information fusion; the author thinks that this is particularly the case in dealing with public risk assessment. A lower probability is undominated if there is no measure whose value for every element of the algebra is greater than the lower probability value. The considerations alluded above call for dominated lower probabilities. But there is a class of phenomena in physics, called flicker phenomena, that only fit uncomfortably into a classical probabilistic framework. The process is stationary, but seems to require limited divergence. Two relevant theorems are stated: One shows that the probability of divergence is 0 in any lower probability model that is dominated; the other shows that undominated lower probability models can support divergence with probability 1. It thus appears that in addition to its obvious usefulness in representing rational epistemic states and the merging of opinions, the theory of lower probabilities may have an application in physics that cannot be dealt with by classical probability theory.
scientific article; zbMATH DE number 4109711
scientific article