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An Object-Oriented Approach to Local Computation in Bayes Linear Belief Networks

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COMPSTAT

Abstract

A generalised conditional independence property based on zero partial correlations can be used to define Bayes linear graphical models, which may then be used as the basis for local computation. As for the full Bayesian case, local computation actually takes place on the clique-tree of the triangulated moral graph. An object-oriented framework for local computation is described which can be implemented via pure message-passing between objects representing adjacent clique-tree nodes. Messages consist of small matrices and vectors containing information about the current observation, making updating and propagation very fast. A sequential implementation, BAYES-LIN, is described.

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References

  • de Finetti, B. (1974). Theory of Probability, Vol. 1. Chichester: Wiley.

    MATH  Google Scholar 

  • Goldstein, M. (1990). Influence and belief adjustment. In: Influence Diagrams, Belief Nets and Decision Analysis. Chichester: Wiley.

    Google Scholar 

  • Goldstein, M. (1997). Prior inferences for posterior judgements. In: Structures and Norms in Science. Pordrecht: Kluwer.

    Google Scholar 

  • Goldstein, M. (1998). Bayes linear analysis. In: Encyclopedia of Statistical Sciences. Update volume 3. Chichester: Wiley.

    Google Scholar 

  • Goldstein, M. & Wilkinson, D.J. (1997). Bayes linear analysis for graphical models: The geometric approach to local computation and interpretive graphics. University of Newcastle, Department of Statistics Preprint, STA97,21.

    Google Scholar 

  • Goldstein, M. & Wooff, D.A. (1995) Bayes linear computation: concepts, implementation and programming environment. Statistics and Computing, 5, 327–341.

    Article  Google Scholar 

  • Lauritzen, S.L. (1992). Propagation of probabilities, means, and variances in mixed graphical association models. Journal of the American Statistical Association, 87 (420), 1098–1108.

    Article  MathSciNet  MATH  Google Scholar 

  • Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann.

    Google Scholar 

  • Smith, J.Q. (1990). Statistical principles on graphs. In: Influence Diagrams, Belief Nets and Decision Analysis. Chichester: Wiley.

    Google Scholar 

  • Tierney, L. (1990). LISP-STAT: An Object-Oriented Environment for Statistical Computing and Dynamic Graphics. Chichester: Wiley.

    Book  MATH  Google Scholar 

  • Wilkinson, D.J. (1997). BAYES-LIN: An object-oriented environment for Bayes linear local computation. University of Newcastle, Department of Statistics Preprint, STA97,20.

    Google Scholar 

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© 1998 Springer-Verlag Berlin Heidelberg

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Wilkinson, D.J. (1998). An Object-Oriented Approach to Local Computation in Bayes Linear Belief Networks. In: Payne, R., Green, P. (eds) COMPSTAT. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-01131-7_70

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  • DOI: https://doi.org/10.1007/978-3-662-01131-7_70

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1131-5

  • Online ISBN: 978-3-662-01131-7

  • eBook Packages: Springer Book Archive

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