Lower probability models for uncertainty and non-deterministic processes
type: Item
instance of: scholarly article
title: Lower probability models for uncertainty and non-deterministic processes
zbMATH Open document ID: 0677.60003
DOI: 10.1016/0378-3758(88)90099-7
author: Terrence L. Fine
published in: Journal of Statistical Planning and Inference
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60A05
zbMATH DE Number: 4109711
zbMATH Keywords: upper and lower probability
zbMATH Keywords: interval valued probability
zbMATH Keywords: non-standard models
zbMATH Keywords: theory of belief functions
zbMATH Keywords: public risk assessment
reviewed by: Henry E. jun. Kyburg
MaRDI profile type: Publication
full work available at URL: 0378-3758(88)90099-7
OpenAlex ID: W1978705670
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Wikidata QID: Q125890144
description: scientific article; zbMATH DE number 4109711