Skip to main content
SpringerLink
Log in

A Continuous Updating Rule for Imprecise Probabilities

  • Conference paper
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 444))

Abstract

The paper studies the continuity of rules for updating imprecise probability models when new data are observed. Discontinuities can lead to robustness issues: this is the case for the usual updating rules of the theory of imprecise probabilities. An alternative, continuous updating rule is introduced.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. de Finetti, B.: Theory of Probability, 2 vols. Wiley (1974-1975)

    Google Scholar 

  2. Savage, L.J.: The Foundations of Statistics, 2nd edn. Dover (1972)

    Google Scholar 

  3. Bhaskara Rao, K.P.S., Bhaskara Rao, M.: Theory of Charges. Academic Press (1983)

    Google Scholar 

  4. Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall (1991)

    Google Scholar 

  5. Cattaneo, M.: On the robustness of imprecise probability methods. In: Cozman, F., Denœux, T., Destercke, S., Seidfenfeld, T. (eds.) ISIPTA 2013, pp. 33–41. SIPTA (2013)

    Google Scholar 

  6. Piatti, A., Zaffalon, M., Trojani, F., Hutter, M.: Limits of learning about a categorical latent variable under prior near-ignorance. Int. J. Approx. Reasoning 50, 597–611 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  7. Walley, P.: Inferences from multinomial data: learning about a bag of marbles. J. R. Stat. Soc., Ser. B 58, 3–57 (1996)

    MATH  MathSciNet  Google Scholar 

  8. Dunford, N., Schwartz, J.T.: Linear Operators, 3 vols. Wiley (1958–1971)

    Google Scholar 

  9. Škulj, D., Hable, R.: Coefficients of ergodicity for Markov chains with uncertain parameters. Metrika 76, 107–133 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fan, K.: Minimax theorems. Proc. Natl. Acad. Sci. USA 39, 42–47 (1953)

    Article  MATH  Google Scholar 

  11. Cattaneo, M.: A generalization of credal networks. In: Augustin, T., Coolen, F.P.A., Moral, S., Troffaes, M.C.M. (eds.) ISIPTA 2009, pp. 79–88, SIPTA (2009)

    Google Scholar 

  12. Moral, S., de Campos, L.M.: Updating uncertain information. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds.) IPMU 1990. LNCS, vol. 521, pp. 58–67. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  13. Moral, S.: Calculating uncertainty intervals from conditional convex sets of probabilities. In: Dubois, D., Wellman, M.P., D’Ambrosio, B., Smets, P. (eds.) UAI 1992, pp. 199–206. Morgan Kaufmann (1992)

    Google Scholar 

  14. Gilboa, I., Schmeidler, D.: Updating ambiguous beliefs. J. Econ. Theory 59, 33–49 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. Moral, S., Wilson, N.: Revision rules for convex sets of probabilities. In: Coletti, G., Dubois, D., Scozzafava, R. (eds.) Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, pp. 113–127. Springer (1995)

    Google Scholar 

  16. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)

    Google Scholar 

  17. Antonucci, A., Cattaneo, M.E.G.V., Corani, G.: Likelihood-based robust classification with Bayesian networks. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012, Part III. CCIS, vol. 299, pp. 491–500. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  18. Cattaneo, M., Wiencierz, A.: Likelihood-based Imprecise Regression. Int. J. Approx. Reasoning 53, 1137–1154 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  19. Destercke, S.: A pairwise label ranking method with imprecise scores and partial predictions. In: Blockeel, H., Kersting, K., Nijssen, S., Železný, F. (eds.) ECML PKDD 2013, Part II. LNCS (LNAI), vol. 8189, pp. 112–127. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  20. Miranda, E.: Updating coherent previsions on finite spaces. Fuzzy Sets Syst. 160, 1286–1307 (2009)

    Article  MATH  Google Scholar 

  21. Cattaneo, M.: Fuzzy probabilities based on the likelihood function. In: Dubois, D., Lubiano, M.A., Prade, H., Gil, M.A., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Handling Variability and Imprecision, pp. 43–50. Springer (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, LMU Munich, Ludwigstraße 33, 80539, München, Germany

    Marco E. G. V. Cattaneo

Authors
  1. Marco E. G. V. Cattaneo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University Montpellier 2, LIRMM - CNRS UMR 5506, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Anne Laurent

  2. Institute for Human Factors and Technology Management, IAT, University of Stuttgart, Nobelstraße 12, 70569, Stuttgart, Germany

    Oliver Strauss

  3. LIP6, UPMC Univ. Paris 06, CNRS UMR 7606, F-75005, Paris, France

    Bernadette Bouchon-Meunier

  4. Dept. of Information Systems, Iona College, 710 North Ave, 10801, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Cattaneo, M.E.G.V. (2014). A Continuous Updating Rule for Imprecise Probabilities. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-319-08852-5_44

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08852-5_44

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08851-8

  • Online ISBN: 978-3-319-08852-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation