Equivalence Between Bayesian and Credal Nets on an Updating Problem

  • Alessandro Antonucci
  • Marco Zaffalon
Part of the Advances in Soft Computing book series (AINSC, volume 37)


We establish an intimate connection between Bayesian and credal nets. Bayesian nets are precise graphical models, credal nets extend Bayesian nets to imprecise probability. We focus on traditional belief updating with credal nets, and on the kind of belief updating that arises with Bayesian nets when the reason for the missingness of some of the unobserved variables in the net is unknown. We show that the two updating problems are formally the same.


Bayesian Network Mass Function Probability Table Markov Condition Imprecise Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Cano, J. Cano, and S. Moral. Convex sets of probabilities propagation by simulated annealing on a tree of cliques. In Proceedings of the Fifth International Conference (IPMU ’94), pages 978–983, Paris, 1994.Google Scholar
  2. [2]
    A. Cano and S. Moral. Using probability trees to compute marginals with imprecise probabilities. Int. J. Approx. Reasoning, 29(1):1–46, 2002.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    F.G. Cozman. Graphical models for imprecise probabilities. Int. J. Approx. Reasoning, 39(2–3):167–184, 2005.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    G. de Cooman and M. Zaffalon. Updating beliefs with incomplete observations. Artificial Intelligence, 159:75–125, 2004.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, 1988.Google Scholar
  6. [6]
    P. Walley. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, New York, 1991.MATHGoogle Scholar
  7. [7]
    M. Zaffalon. Conservative rules for predictive inference with incomplete data. In F.G. Cozman, R. Nau, and T. Seidenfeld, editors, Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications (ISIPTA ’05), pages 406–415, Pittsburgh, 2005.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Alessandro Antonucci
    • 1
  • Marco Zaffalon
    1. 1.Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA)Manno (Lugano)Switzerland

    Personalised recommendations