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Bayesian approximation and invariance of Bayesian belief functions

  • A. V. Joshi
  • S. C. Sahasrabudhe
  • K. Shankar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 946)

Abstract

The Dempster-Shafer theory is being applied for handling uncertainty in various domains. Many methods have been suggested in the literature for faster computation of belief which is otherwise exponentially complex. Bayesian approximation is one such method. In this paper, we first present some results on invariance of Bayesian belief functions under Dempster's combination rule. Based on this, we interpret Bayesian approximation and further show that it inherits these properties from the combination operator of Dempster's combination rule. Finally, we bring into focus the limitation of Bayesian approximation.

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References

  1. 1.
    Barnett, J.: Computational methods for a mathematical theory of evidence, in Proceedings IJCAI-81, Vancouver, BC (1981) 868–875.Google Scholar
  2. 2.
    Dubois, D., Prade, H.: Consonant approximations of belief functions. Int. J. Approx. Reasoning. 4 (1990) 419–449.Google Scholar
  3. 3.
    Gordon, J., Shortliffe, E.: A method for managing evidential reasoning in a hierarchical hypothesis space. Artificial Intelligence. 26 (1985) 323–357.MathSciNetGoogle Scholar
  4. 4.
    Kennes, R., Smets, P.: Fast algorithms for Dempster-Shafer theory, in: Bouchon-Meunier B., Yager R.R., and Zadeh L. (eds.) Uncertainty in Knowledge Bases. Lecture Notes in Computer Science. 521 (Springer, Berlin, 1991) 14–23.Google Scholar
  5. 5.
    Kennes, R., Smets, P.: Computational aspects of the möbius transformation, in: Bonnisonne P.P., Henrion M., Kanal L.N. and Lemmer J.F. (eds.) Uncertainty in Artificial Intelligence. 6 (North-Holland, Amsterdam, 1991) 401–416.Google Scholar
  6. 6.
    Kohlas, J., Monney, P.: Propagating belief functions through constraints system, in: Bouchon-Meunier B., Yager R.R., and Zadeh L. (eds.) Uncertainty in Knowledge Bases. Lecture Notes in Computer Science. 521 (Springer, Berlin, 1991) 50–57.Google Scholar
  7. 7.
    Shafer, G.: A Mathematical Theory of Evidence (Princeton University Press, Princeton, NJ, 1976).Google Scholar
  8. 8.
    Shafer, G., Logan, R.: Implementing Dempster's rule for hierarchical evidence. Artificial Intelligence. 33 (1987) 271–298.CrossRefGoogle Scholar
  9. 9.
    Shafer, G.,Shenoy, P., Mellouli, K.: Propagating belief functions in qualitative markov trees. Int. J. Approx. Reasoning. 1, (1987) 349–400.Google Scholar
  10. 10.
    Shenoy, P., Shafer, G.: Propagating belief functions with local computations, IEEE Expert. 1:3 (1986) 43–52.Google Scholar
  11. 11.
    Smets, P.: Belief functions versus probability functions, in: Bouchon B., Saitta L. and Yager R. (eds.) Uncertainty and Intelligent Systems. Lecture Notes in Computer Science. 313 (Springer, Berlin, 1988) 17–24.Google Scholar
  12. 12.
    Smets, P.: Constructing the pignistic probability function in a context of uncertainty, in: Henrion M., Shachter R.D., Kanal L.N. and Lemmer J.F. (eds.) Uncertainty in Artificial Intelligence. 5 (North-Holland, Amsterdam, 1990) 29–39.Google Scholar
  13. 13.
    Tessem, B.: Approximations for efficient computation in the theory of evidence. Artificial Intelligence. 61 (1993) 315–329.Google Scholar
  14. 14.
    Voorbraak, F.: A computationally efficient approximation of Dempster-Shafer theory. Int. J. Man-Mach. Stud. 30 (1989) 525–536.Google Scholar
  15. 15.
    Wilson, N.: The combination of belief: when and how fast?, Int. J. Approx. Reasoning. 6 (May 1992) 377–388.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • A. V. Joshi
    • 1
  • S. C. Sahasrabudhe
    • 1
  • K. Shankar
    • 1
  1. 1.Electrical Engineering DepartmentIndian Institute of TechnologyPowai, BombayIndia

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