Skip to main content
SpringerLink
Log in

Stochastic Independence in a Coherent Setting

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

Our aim is to put under the right perspective the theory of stochastic independence in the framework of coherent probability theory, taking suitably into account also events whose probability is zero or one. Moreover, in a coherent setting, upper and lower probabilities come naturally to the fore, and so we discuss the issues raised when trying to extend stochastic independence to this more general concept.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Capotorti and B. Vantaggi, Locally strong coherence in inference processes, Annals of Mathematics and Artificial Intelligence, this issue.

  2. A. Capotorti, L. Galli and B. Vantaggi, How to use locally strong coherence in inferential processes based on lower-upper probabilities, Soft Computing (2001) in press.

  3. G. Coletti, Coherent numerical and ordinal probabilistic assessments, IEEE Transactions on Systems, Man, and Cybernetics 24 (1994) 1747-1754.

    Google Scholar 

  4. G. Coletti, A. Gilio and R. Scozzafava, Conditional events with vague information in expert systems, in: Lecture Notes in Computer Sciences, Vol. 521, eds. B. Bouchon-Meunier, R.R. Yager and L.A. Zadeh (Springer, Berlin, 1991) pp. 106-114.

    Google Scholar 

  5. G. Coletti and R. Scozzafava, Characterization of coherent conditional probabilities as a tool for their assessment and extension, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 4 (1996) 103-127.

    Google Scholar 

  6. G. Coletti and R. Scozzafava, Conditional measures: old and new, in: Proceedings of New Trends in Fuzzy Systems, Napoli, 1996, eds. D. Mancini, M. Squillante and A. Ventre (World Scientific, Singapore, 1998) pp. 107-120.

    Google Scholar 

  7. G. Coletti and R. Scozzafava, Null events and stochastical independence, Kybernetika 34 (1998) 69-78.

    Google Scholar 

  8. 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, Selected papers from IPMU 1998 (Kluwer, Dordrecht, 2000) pp. 185-196.

    Google Scholar 

  9. G. Coletti and R. Scozzafava, Conditioning and inference in intelligent systems, Soft Computing 3 (1999) 118-130.

    Google Scholar 

  10. G. Coletti and R. Scozzafava, The role of coherence in eliciting and handling "imprecise" probabilities and its application to medical diagnosis, Information Sciences 130 (2000) 41-65.

    Google Scholar 

  11. G. Coletti and R. Scozzafava, Stochastic independence for upper and lower probabilities in a coherent setting, in: Technologies for Constructing Intelligent Systems, Vol. 2, eds. B. Bouchon-Meunier, J. Gutiérrez-Rios, L. Magdalena, and R.R. Yager, Selected papers from IPMU 2000 (Springer, Berlin, 2001).

    Google Scholar 

  12. G. Coletti and R. Scozzafava, From conditional events to conditional measures: a new axiomatic approach, Annals of Mathematics and Artificial Intelligence 32, Special Issue on Representation of Uncertainty, ed. H. Greenberg (2001) 373-392.

    Google Scholar 

  13. G. Coletti, R. Scozzafava and B. Vantaggi, Probabilistic reasoning as a general unifying tool, in: Lecture Notes in Artificial Intelligence, Vol. 2143, eds. S. Benferhat and P. Besnard (Springer, Berlin, 2001) pp. 120-131.

    Google Scholar 

  14. I. Couso, S. Moral and P. Walley, Examples of independence for imprecise probabilities, in: International Symposium on Imprecise Probabilities and their Applications (ISIPTA '99) Ghent, Belgium (1999) pp. 121-130.

  15. L.M. De Campos and S. Moral, Independence concepts for convex sets of probabilities, in: Uncertainty in Artificial Intelligence (UAI '95) (Morgan Kaufmann, San Mateo, CA, 1995) pp. 108-115.

    Google Scholar 

  16. B. de Finetti, Les probabilités nulles, Bulletin des Sciences Mathématiques 60 (1936) 275-288.

    Google Scholar 

  17. B. de Finetti, Sull'impostazione assiomatica del calcolo delle probabilità. Annali Univ. Trieste 19 (1949) 3-55. English translation in: Probability, Induction, Statistics (Wiley, London, 1972) chapter 5.

    Google Scholar 

  18. L.E. Dubins, Finitely additive conditional probabilities, conglomerability and disintegration, The Annals of Probability 3 (1975) 89-99.

    Google Scholar 

  19. P.H. Krauss, Representation of conditional probability measures on Boolean algebras, Acta Mathematica Hungarica 19 (1968) 229-241.

    Google Scholar 

  20. A. Rényi, On conditional probability spaces generated by a dimensionally ordered set of measures, Theory of Probability and its Applications 1 (1956) 61-71.

    Google Scholar 

  21. B. Vantaggi, Conditional independence in a finite coherent setting, Annals of Mathematics and Artificial Intelligence 32, Special Issue on Representation of Uncertainty, ed. H. Greenberg (2001) 287-313.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Perugia, Perugia, Italy

    G. Coletti

  2. Dipartimento Metodi e Modelli Matematici, Università “La Sapienza”, Roma, Italy

    R. Scozzafava

Authors
  1. G. Coletti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Scozzafava
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Coletti, G., Scozzafava, R. Stochastic Independence in a Coherent Setting. Annals of Mathematics and Artificial Intelligence 35, 151–176 (2002). https://doi.org/10.1023/A:1014535200933

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014535200933

Search

Navigation