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Event‐Tree Analysis with Imprecise Probabilities
Author(s) -
You Xiaomin,
To Fulvio
Publication year - 2012
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/j.1539-6924.2011.01721.x
Subject(s) - event (particle physics) , conditional probability , event tree , mathematics , tree (set theory) , law of total probability , bounded function , set (abstract data type) , imprecise probability , event tree analysis , statistics , tree diagram , upper and lower bounds , probability distribution , probability measure , convex combination , measure (data warehouse) , regular conditional probability , posterior probability , regular polygon , combinatorics , probability mass function , computer science , data mining , fault tree analysis , bayesian probability , convex optimization , mathematical analysis , engineering , geometry , quantum mechanics , reliability engineering , programming language , physics
Novel methods are proposed for dealing with event‐tree analysis under imprecise probabilities, where one could measure chance or uncertainty without sharp numerical probabilities and express available evidence as upper and lower previsions (or expectations) of gambles (or bounded real functions). Sets of upper and lower previsions generate a convex set of probability distributions (or measures). Any probability distribution in this convex set should be considered in the event‐tree analysis. This article focuses on the calculation of upper and lower bounds of the prevision (or the probability) of some outcome at the bottom of the event‐tree. Three cases of given information/judgments on probabilities of outcomes are considered: (1) probabilities conditional to the occurrence of the event at the upper level; (2) total probabilities of occurrences, that is, not conditional to other events; (3) the combination of the previous two cases. Corresponding algorithms with imprecise probabilities under the three cases are explained and illustrated by simple examples.