Role of coherence in eliciting and handling imprecise probabilities and its application to medical diagnosis

Information sciences

Volumn 130, Issue 1-4, 2000, Pages 41-65

  Coletti, Giulianella ^a   Scozzafava, Romano ^b  

^a UNIVERSITY OF PERUGIA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL LINGUISTICS; DATA HANDLING; DATA STRUCTURES; DECISION THEORY; PROBABILITY DISTRIBUTIONS;

BAYES THEORY;

DATA COMMUNICATION SYSTEMS;

EID: 0034497110     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-0255(00)00085-2     Document Type: Article

References (41)

1. Berger J.O. Statistical Decision Theory. 1980;Springer, New York.
2. Bernardo J.M., Smith A.F.M. Bayesian Theory. 1993;Wiley, New York.
3. A. Capotorti, B. Vantaggi, An algorithm for coherent conditional probability assessments, in: Proceedings of the IV Congresso Nazionale SIMAI, vol. 2, Giardini Naxos, Italy, 1998, pp. 144-148.
4. A. Capotorti, S. Tognoloni, B. Vantaggi, Local coherence of conditional probabilities assessments: definition and application, Rapp. Tecn. n.10, Dip. Matem., University of Perugia, Italy, 1999.
5. A. Capotorti, L. Galli, B. Vantaggi, How to use strong local coherence in an inferential process based on upper-lower probabilities, WUPES 2000, Jindrichuv Hradec (Praha), 2000, pp. 14-28 (to appear in Soft Computing).
6. Coletti G. Coherent numerical and ordinal probabilistic assessments. IEEE Trans. Syst., Man Cybernet. 24:1994;1747-1754.
7. G. Coletti, A. Gilio, R. Scozzafava, Conditional events with vague information in expert systems, in: B. Bouchon-Meunier, R.R. Yager, L.A. Zadeh (Eds.), Lecture Notes in Computer Sciences, vol. 521, Springer, Berlin, 1991, pp. 106-114.
8. G. Coletti, R. Scozzafava, Learning from data by coherent probabilistic reasoning, in: B.M. Ayyub (Ed.), Proceedings of the Third International Symposium on Uncertainty Modeling and Analysis, Maryland, IEEE Computer Society Press, Silver Spring, MD, 1995, pp. 535-540.
9. Coletti G., Scozzafava R. Characterization of coherent conditional probabilities as a tool for their assessment and extension. Int. J. Uncertain. Fuzziness Knowledge-Based Syst. 4:1996;103-127.
10. G. Coletti, R. Scozzafava, Conditional measures: old and new, in: D. Mancini, M. Squillante, A. Ventre (Eds.), Procedings of New Trends in Fuzzy Systems, Napoli 1996. World Scientific, Singapore, 1998, pp. 107-120.
11. G. Coletti, R. Scozzafava, Exploiting zero probabilities, in: Proceedings of EUFIT '97, Elite Foundation, Aachen, 1997, pp. 1499-1503.
12. G. Coletti, R. Scozzafava, Medical diagnosis by coherent probabilistic reasoning (Abstract), in: Proceedings of the Fourth International Congress on Industrial and Applied Mathematics (ICIAM '99), Edinburgh, 1999, p. 307.
13. G. Coletti, R. Scozzafava, Conditional subjective probability and fuzzy theory, in: Proceedings of the 18th International Conference of NAFIPS, New York, 1999, p. 77-80.
14. Coletti G., Scozzafava R. Conditioning and inference in intelligent systems. Soft Comput. 3:1999;118-130.
15. G. Coletti, R. Scozzafava, Coherent upper and lower probabilities, in: Proceedings of the First International Symposium on Imprecise Probabilities and their Applications (ISIPTA), Ghent, 1999, pp. 101-110.
16. G. Coletti, R. Scozzafava, Zero probabilities in stochastic independence. In: B. Bouchon-Meunier, R.R. Yager, L.A. Zadeh (Eds.), Information, Uncertainty, Fusion, Kluwer, Dordrecht, 2000, pp. 185-196 (selected papers from IPMU '98, Paris).
17. B. de Finetti, Teoria della probabilità. Einaudi, Torino, 1970. (Engl. transl.: Theory of Probability. Wiley, Chichester, 1974).
18. B. de Finetti, Sull'impostazione assiomatica del calcolo delle probabilità. Ann. Univ. Trieste Vol. 19, 1949, pp. 3-55 (Engl. transl.: chapter 5 in Probability, Induction, Statistics, Wiley, London, 1972).
19. Dubins L.E. Finitely additive conditional probabilities, conglomerability and disintegration. Ann. Probab. 3:1975;89-99.
20. French S. Decision Theory: An Introduction to the Mathematics of Rationality. 1988;Ellis, Chichester.
21. Gilio A. Criterio di penalizzazione e condizioni di coerenza nella valutazione soggettiva della probabilitá Boll. Un. Mat. Ital. B. 7(4):1990;645-660.
22. Gilio A., Ingrassia S. Totally coherent set-valued probability assessments. Kybernetika (Prague). 34:1998;3-15.
23. Hartigan J.A. Bayes Theory. 1983;Springer, New York.
24. Hoel P.G., Port S.C., Stone C.J. Introduction to Probability Theory. 1971;Houghton Mifflin, Boston.
25. Holzer S. On coherence and conditional prevision. Boll. Un. Mat. Ital. 6(4):1985;441-460.
26. Kalbfleisch J.G. Probability and Statistical Inference. 1979;Springer, New York.
27. Krauss P.H. Representation of conditional probability measures on Boolean algebras. Acta Math. Acad. Sci. Hungar. 19:1968;229-241.
28. Lad F. Operational Subjective Statistical Methods. 1996;Wiley, New York.
29. Lee P.M. Bayesian Statistics: An Introduction. 1989;Arnold, Paris.
30. Lehman R.S. On confirmation and rational betting. J. Symbolic Logic. 20:1955;251-262.
31. Lindley D.V. Introduction to Probability and Statistics from a Bayesian Viewpoint. 1969;Cambridge University Press, Cambridge.
32. Lindley D.V. Bayesian Statistics: A Review. 1972;SIAM, Philadelphia.
33. Phillips L.D. Bayesian Statistics for Social Scientists. 1973;Nelson, London.
34. Press S.J. Bayesian Statistics: Principles, Models, and Applications. 1989;Wiley, New York.
35. Regazzini E. Finitely additive conditional probabilities. Rend. Sem. Mat. Fis. Milano. 55:1985;69-89.
36. Rényi A. On conditional probability spaces generated by a dimensionally ordered set of measures. Theor. Prob. Appl. 1:1956;61-71.
37. Savage L.J. The Foundations of Statistics. 1972;Dover, New York.
38. Smith C.B.A. Consistency in statistical inference and decision. J. Roy. Stat. Soc. B. 23:1961;1-37.
39. Walley P. Statistical Reasoning with Imprecise Probabilities. 1991;Chapman and Hall, London.
40. P.M. Williams, Notes on conditional previsions. Working paper, School of Mathematical and Physical Sciences, University of Sussex, UK, 1975.
41. P.M. Williams, Indeterminate probabilities. in: M. Przelecki, K. Szaniawski, R. Vojcicki (Eds.), Formal Methods in the Methodology of Empirical Sciences. Reidel, Dordrecht, 1976, pp. 229-246.