Abstract
There are many ways to extend the classical expected utility decision rule to the case where uncertainty is described by (convex) probability sets. In this paper, we propose a simple new decision rule based on the pair-wise comparison of lower and upper expected bounds. We compare this rule to other rules proposed in the literature, showing that this new rule is both precise, computationally tractable and can help to boost the computation of other, more computationally demanding rules.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
de Cooman, G., Troffaes, M.C.M.: Dynamic programming for deterministic discrete-systems with uncertain gain. Internat. J. Approx. Reason. 39, 257–278 (2004)
Finetti, B.: Theory of probability, vol 1(2). Wiley, NY (1974) (translation of 1970 book)
Gilboa, I., Schmeidler, D.: Maxmin expected utility with non-unique prior. J. Math. Econom. 18(2), 141–153 (1989)
Jaffray, J.Y., Jeleva, M.: Information processing under imprecise risk with the Hurwicz criterion. In: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications, ISIPTA 2007, Prague, Czech Republic, pp. 233–254 (2007)
Levi, I.: The Enterprise of Knowledge. MIT Press, London (1980)
Troffaes, M.: Decision making under uncertainty using imprecise probabilities. Internat. J. Approx. Reason. 45, 17–29 (2007)
Utkin, L., Augustin, T.: Powerful algorithms for decision making under partial prior information and general ambiguity attitudes. In: Proceedings of the Fourth International Symposium on Imprecise Probability: Theories and Applications, ISIPTA 2005, pp. 349–358. Carnegie Mellon University, Pittsburgh (2005)
von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)
Walley, P.: Statistical reasoning with imprecise Probabilities. Chapman and Hall, New York (1991)
Zaffalon, M.: The naive credal classifier. Imprecise probability models and their applications (Ghent, 1999). J. Statist. Plann. Inference 105(1), 5–21 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Destercke, S. (2010). A Decision Rule for Imprecise Probabilities Based on Pair-Wise Comparison of Expectation Bounds. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-14746-3_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14745-6
Online ISBN: 978-3-642-14746-3
eBook Packages: EngineeringEngineering (R0)