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Propagating imprecise probabilities through event trees

Gert De Cooman (UGent) , Filip Hermans (UGent) and Erik Quaeghebeur (UGent)
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Abstract
Event trees are a graphical model of a set of possible situations and the possible paths going through them, from the initial situation to the terminal situations. With each situation, there is associated a local uncertainty model that represents beliefs about the next situation. The uncertainty models can be classical, precise probabilities; they can also be of a more general, imprecise probabilistic type, in which case they can be seen as sets of classical probabilities (yielding probability intervals). To work with such event trees, we must combine these local uncertainty models. We show this can be done efficiently by back-propagation through the tree, both for precise and imprecise probabilistic models, and we illustrate this using an imprecise probabilistic counterpart of the classical Markov chain. This allows us to perform a robustness analysis for Markov chains very efficiently.

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Chicago
De Cooman, Gert, Filip Hermans, and Erik Quaeghebeur. 2007. “Propagating Imprecise Probabilities Through Event Trees.” In Interuniversity Attraction Pole IAP VI/4 Kickoff Meeting, Posters.
APA
De Cooman, Gert, Hermans, F., & Quaeghebeur, E. (2007). Propagating imprecise probabilities through event trees. Interuniversity Attraction Pole IAP VI/4 Kickoff meeting, Posters. Presented at the Interuniversity Attraction Pole IAP VI/4 Kickoff meeting.
Vancouver
1.
De Cooman G, Hermans F, Quaeghebeur E. Propagating imprecise probabilities through event trees. Interuniversity Attraction Pole IAP VI/4 Kickoff meeting, Posters. 2007.
MLA
De Cooman, Gert, Filip Hermans, and Erik Quaeghebeur. “Propagating Imprecise Probabilities Through Event Trees.” Interuniversity Attraction Pole IAP VI/4 Kickoff Meeting, Posters. 2007. Print.
@inproceedings{1974570,
  abstract     = {Event trees are a graphical model of a set of possible situations and the possible paths going through them, from the initial situation to the terminal situations. With each situation, there is associated a local uncertainty model that represents beliefs about the next situation. The uncertainty models can be classical, precise probabilities; they can also be of a more general, imprecise probabilistic type, in which case they can be seen as sets of classical probabilities (yielding probability intervals). To work with such event trees, we must combine these local uncertainty models. We show this can be done efficiently by back-propagation through the tree, both for precise and imprecise probabilistic models, and we illustrate this using an imprecise probabilistic counterpart of the classical Markov chain. This allows us to perform a robustness analysis for Markov chains very efficiently.},
  author       = {De Cooman, Gert and Hermans, Filip and Quaeghebeur, Erik},
  booktitle    = {Interuniversity Attraction Pole IAP VI/4 Kickoff meeting, Posters},
  language     = {eng},
  location     = {Louvain-la-Neuve, Belgium},
  title        = {Propagating imprecise probabilities through event trees},
  year         = {2007},
}