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Sensitivity Statistical Estimates for Local A Posteriori Inference Matrix-Vector Equations in Algebraic Bayesian Networks over Quantum Propositions

Abstract

An approach to the sensitivity analysis of local a posteriori inference equations in algebraic Bayesian networks is proposed in this paper. Some basic definitions and formulations are briefly given and the development of the matrix-vector a posteriori inference approach is considered. Some cases of the propagation of deterministic and stochastic evidence in a knowledge pattern with scalar estimates of component truth probabilities over quantum propositions are described. For each of the considered cases, the necessary metrics are introduced, and some transformations resulting in four linear programming problems are performed. The solution of these problems gives the required estimates. In addition, two theorems postulating the covering estimates for the considered parameters are formulated. The results obtained in this work prove the correct application of models and create a basis for the sensitivity analysis of local and global probabilistic-logic inference equations.

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Correspondence to A. A. Zolotin.

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Original Russian Text © A.A. Zolotin, A.L. Tulupyev, 2018, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2018, Vol. 63, No. 1, pp. 55–64.

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Zolotin, A.A., Tulupyev, A.L. Sensitivity Statistical Estimates for Local A Posteriori Inference Matrix-Vector Equations in Algebraic Bayesian Networks over Quantum Propositions. Vestnik St.Petersb. Univ.Math. 51, 42–48 (2018). https://doi.org/10.3103/S1063454118010168

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Keywords

  • uncertain knowledge
  • propagation of evidence
  • probabilistic logic
  • algebraic Bayesian networks
  • probabilistic-logic inference
  • sensitivity statistical estimates
  • probabilistic graphical models
  • matrix-vector equations