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Event‐Tree Analysis with Imprecise Probabilities

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  • Xiaomin You
  • Fulvio Tonon

Abstract

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.

Suggested Citation

  • Xiaomin You & Fulvio Tonon, 2012. "Event‐Tree Analysis with Imprecise Probabilities," Risk Analysis, John Wiley & Sons, vol. 32(2), pages 330-344, February.
    • Handle: RePEc:wly:riskan:v:32:y:2012:i:2:p:330-344
    DOI: 10.1111/j.1539-6924.2011.01721.x
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    References listed on IDEAS

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    1. A. Bernardini & F. Tonon, 2009. "Extreme probability distributions of random sets, fuzzy sets and p-boxes," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 3(1/2/3), pages 57-78.
    2. Couso, Ines & Moral, Serafin & Walley, Peter, 2000. "A survey of concepts of independence for imprecise probabilities," Risk, Decision and Policy, Cambridge University Press, vol. 5(2), pages 165-181, June.
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    Cited by:

    1. Elena M. Parilina & Georges Zaccour, 2022. "Sustainable Cooperation in Dynamic Games on Event Trees with Players’ Asymmetric Beliefs," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 92-120, July.

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