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A survey of concepts of independence for imprecise probabilities

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  • COUSO, INES
  • MORAL, SERAFIN
  • WALLEY, PETER

Abstract

Our aim in this paper is to clarify the notion of independence for imprecise probabilities. Suppose that two marginal experiments are each described by an imprecise probability model, i.e., by a convex set of probability distributions or an equivalent model such as upper and lower probabilities or previsions. Then there are several ways to define independence of the two experiments and to construct an imprecise probability model for the joint experiment. We survey and compare six definitions of independence. To clarify the meaning of the definitions and the relationships between them, we give simple examples which involve drawing balls from urns. For each concept of independence, we give a mathematical definition, an intuitive or behavioural interpretation, assumptions under which the definition is justified, and an example of an urn model to which the definition is applicable. Each of the independence concepts we study appears to be useful in some kinds of application. The concepts of strong independence and epistemic independence appear to be the most frequently applicable.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:rdepol:v:5:y:2000:i:02:p:165-181_00
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    Cited by:

    1. Dubois, Didier, 2006. "Possibility theory and statistical reasoning," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 47-69, November.
    2. Sébastien Destercke, 2017. "On the median in imprecise ordinal problems," Annals of Operations Research, Springer, vol. 256(2), pages 375-392, September.
    3. Xiaomin You & Fulvio Tonon, 2012. "Event‐Tree Analysis with Imprecise Probabilities," Risk Analysis, John Wiley & Sons, vol. 32(2), pages 330-344, February.
    4. Nicola Pedroni & Enrico Zio, 2013. "Uncertainty Analysis in Fault Tree Models with Dependent Basic Events," Risk Analysis, John Wiley & Sons, vol. 33(6), pages 1146-1173, June.
    5. Vorobyev, Oleg, 2009. "Eventology versus contemporary theories of uncertainty," MPRA Paper 13961, University Library of Munich, Germany.
    6. Stavros Lopatatzidis & Jasper Bock & Gert Cooman & Stijn Vuyst & Joris Walraevens, 2016. "Robust queueing theory: an initial study using imprecise probabilities," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 75-101, February.
    7. Jon T Selvik & Eirik B Abrahamsen, 2017. "On the meaning of accuracy and precision in a risk analysis context," Journal of Risk and Reliability, , vol. 231(2), pages 91-100, April.

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