Conditional independence in a coherent finite setting

Annals of Mathematics and Artificial Intelligence

Volumn 32, Issue 1-4, 2001, Pages 287-313

  Vantaggi, Barbara ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Coherent probability assessment; Conditional independence; Graphoid; Independence model

Indexed keywords

EID: 0035636114     PISSN: 10122443     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016730003879     Document Type: Article

References (22)

1. P. Billingsley, Probability and Measure (Wiley, New York, 1995).
2. G. Coletti, Coherent numerical and ordinal probabilistic assessments, IEEE Trans. Systems, Man, Cybernetics 24(12) (1994) 1747-1754.
3. G. Coletti, Updating and extension of coherent conditional probabilities, in: Proc. of the American Statist. Assoc. Conf., Section on Bayesian Statist. Science, Chicago (1996) pp. 36-41.
4. G. Coletti and R. Scozzafava, Characterization of coherent conditional probabilities as a tool for their assessment and extension, Internat. J. Uncertainty, Fuzziness and Knowledge-Based System 4(2) (1996) 103-127.
5. G. Coletti and R. Scozzafava, Null events and stochastical independence, Kibernetika 34(1) (1998) 69-78.
6. G. Coletti and R. Scozzafava, Zero probabilities in stochastic independence, in: Information, Uncertainty, Fusion, eds. B. Bouchon-Meunier, R.R. Yager and L.A. Zadeh (Kluwer, Dordrecht, 2000) pp. 185-196 (selected papers from IPMU '98).
7. G. Coletti and R. Scozzafava, Conditioning and inference in intelligent systems, Soft Computing 3 (1999) 118-130.
8. L. Crisma, The notion of stochastic independence in the theory of coherent probabilities, Technical Report 1/99, Dipartimento di Matematica applicata "B. de Finetti", University of Trieste (1999).
9. A.P. Dawid, Conditional independence in statistical theory, J. Roy. Statist. Soc. B 41 (1979) 15-31.
10. F.T. de Dombal and F. Gremy (eds.), Decision Making and Medical Care (North-Holland, 1976).
11. B. de Finetti, Sull'impostazione assiomatica del calcolo delle probabilitá, Annali dell'Universitá di Trieste 19 (1949) 3-55. Eng. transl: Ch. 5 in Probability, Induction, Statistics (Wiley, London, 1972).
12. L.E. Dubins, Finitely additive conditional probabilities, conglomerability and disintegration, Ann. Probab. 3 (1975) 89-99.
13. P. Hajek, T. Havranek and R. Jirousek, Uncertain Information Processing in Expert Systems (CRC Press, Boca Raton, FL, 1992).
14. J.R. Hill, Comment on "Graphical models", Statist. Sci. 8 (1993) 258-261.
15. P.H. Krauss, Representation of conditional probability measures on Boolean algebras, Acta Math. Acad. Scient. Hungar 19 (1968) 229-241.
16. S.L. Lauritzen, Graphical Models (Clarendon Press, Oxford, 1996).
17. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (Morgan Kaufmann, San Mateo, CA, 1988).
18. A. Rényi, On conditional probability spaces generated by a dimensionally ordered set of measures, Theor. Probab. Appl. 1 (1956) 61-71.
19. R. Scozzafava, Subjective conditional probability and coherence principles for handling partial information, Mathware & Soft Computing 3 (1996) 183-192.
20. M. Studeny and R.R. Bouckaert, On chain graph models for description of conditional independence structures, Ann. Statist. 26 (4) (1998) 1434-1495.
21. B. Vantaggi, Conditional independence and graphical models in a coherent setting, PhD thesis, Università di Perugia, Italy (1999).
22. J. Witthaker, Graphical Models in Applied Multivariate Statistic (Wiley, New York, 1990).