Abstract
In this paper we propose a way to restrict extension bounds induced by coherent conditional lower-upper probability assessments. Such shrinkage turns out to be helpful whenever the natural bounds are too vague to be used. Since coherence of a conditional lower-upper probability assessment can be characterized through a class of conditional probability distributions, the idea is to take the intersection of the extension bounds induced by each single element of the class instead of the convex combination, as it is usually done. Coherence of such method is proved for extensions performed on both conditional events logical dependent and not-dependent on the initial domain.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Capotorti, A.: Generalized concept of atoms for conditional events. In: Coletti, G., et al. (eds.) Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, pp. 183–189. Plenum Press, New York (1995)
Capotorti, A., Fagundes Leite, S.: Reliability of GIST diagnosis based on partial information. In: Di Bacco, M., D’Amore, G., Scalfari, F. (eds.) Applied Bayesian Statistical Studies In Biology And Medicine. Kluwer Academic Publishers, Boston (2003)
Capotorti, A., Galli, L., Vantaggi, B.: How to use locally strong coherence in an inferential process based on upper-lower probabilities. Soft Computing 7(5), 280–287 (2003)
Capotorti, A., Paneni, T.: An operational view of coherent conditional previsions, in. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 132–143. Springer, Heidelberg (2001)
Capotorti, A.: Benefits of embedding structural constraints in coherent diagnostic processes, International Journal of Approximate Reasoning, article in press corrected proof (2004), available at http://authors.elsevier.com/sd/article/S0888613X04001070
Coletti, G., Scozzafava, R.: Characterization of Coherent Conditional Probabilities as a Tool for their Assessment and Extension. Int. Journ. of Uncertainty, Fuzziness and Knowledge-Based Systems 4(2), 103–127 (1996)
Coletti, G., Scozzafava, R.: Conditional measures: old and new. In: New trends in Fuzzy Systems, pp. 107–120. World Scientific, Singapore (1998)
Coletti, G., Scozzafava, R.: Conditioning and Inference in Itelligent Systems. Soft Computing 3, 118–130 (1999)
Coletti, G., Scozzafava, R.: Probabilistic Logic in a Coherent Setting. “Trends in Logic”. Kluwer, Dordrecht (2002)
de Finetti, B.: Teoria della probabilità, Einaudi, Torino (Engl. transl.: Theory of Probability, vol.1&2. Wiley, Chichester (1970)
Gilio, A.: Algorithms for precise and imprecise conditional probability assessments. In: Coletti, G., et al. (eds.) Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, pp. 231–254. Plenum Press, New York (1995)
The International Society for Imprecise Probability Theory and Applications (eletronic versions). In: Proocedings of the International Symposia on Imprecise Probabilities and Their Applications, http://www.sipta.org/isipta/
Lad, F.: Operational Subjective Statistical Methods: a mathematical, philosophical, and historical introduction. John Wiley, New York (1996)
Walley, P.: Statistical reasoning with Imprecise Probabilities. Chapman and Hall, London (1991)
Walley, P., Pelessoni, R., Vicig, P.: Direct Algorithms for Checking Coherence and Making Inferences from Conditional Probability Assessments. Journal of Statistical Planning and Inference 126(1), 119–151 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Capotorti, A., Zagoraiou, M. (2005). Coherent Restrictions of Vague Conditional Lower-Upper Probability Extensions. In: Godo, L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2005. Lecture Notes in Computer Science(), vol 3571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11518655_63
Download citation
DOI: https://doi.org/10.1007/11518655_63
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27326-4
Online ISBN: 978-3-540-31888-0
eBook Packages: Computer ScienceComputer Science (R0)