Abstract
We relate the epistemic irrelevance in Walley’s behavioural theory of imprecise probabilities to the event-tree independence due to Shafer. In particular, we show that forward irrelevance is equivalent to event-tree independence in particular event trees, suitably generalised to allow for the fact that imprecise rather than precise probability models are attached to the nodes in the tree. This allows us to argue that in a theory of uncertain processes, the asymmetrical notion of epistemic irrelevance has a more important role to play than its more involved and symmetrical counterpart called epistemic independence.
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References
Couso, I., Moral, S., Walley, P.: Examples of independence for imprecise probabilities. Risk Decis Policy 5, 165–181 (2000)
Cozman, F.G.: Credal networks. Artificial Intelligence 120, 199–233 (2000)
Cozman, F.G.: Graphical models for imprecise probabilities. Internat. J. Approx. Reason 39(2-3), 167–184 (2005)
De Cooman, G., Hermans, F.: On coherent immediate prediction: Connecting two theories of imprecise probability. In: De Cooman, G., Vejnarova, J., Zaffalon, M. (eds.) Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2007, Prague, Czech Republic), SIPTA, pp. 107–116 (2007)
De Cooman, G., Hermans, F.: Imprecise probability trees: Bridging two theories of imprecise probability. Artificial Intelligence (in press, 2008) doi:10.1016/j.artint.2008.03.001
De Cooman, G., Miranda, E.: Forward irrelevance. J. Statist. Plan Infer. (in press, 2008a) doi:10.1016/j.jspi.2008.01.012
De Cooman, G., Miranda, E.: Weak and strong laws of large numbers for coherent lower previsions. J. Statist. Plan Infer. (in press, 2008b)doi:10.1016/j.jspi.2007.10.020
Levi, I.: The Enterprise of Knowledge. MIT Press, London (1980)
Miranda, E., De Cooman, G.: Marginal extension in the theory of coherent lower previsions. Internat. J. Approx. Reason 46(1), 188–225 (2007)
Shafer, G.: Conditional probability. Internat. Statist. Rev. 53, 261–277 (1985)
Shafer, G.: The Art of Causal Conjecture. MIT Press, Cambridge (1996)
Shafer, G., Vovk, V.: Probability and Finance: It’s Only a Game! Wiley, New York (2001)
Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)
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© 2008 Springer-Verlag Berlin Heidelberg
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Destercke, S., de Cooman, G. (2008). Relating Epistemic Irrelevance to Event Trees. In: Dubois, D., Lubiano, M.A., Prade, H., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds) Soft Methods for Handling Variability and Imprecision. Advances in Soft Computing, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85027-4_9
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DOI: https://doi.org/10.1007/978-3-540-85027-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85026-7
Online ISBN: 978-3-540-85027-4
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