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

  • A. A. ZolotinEmail author
  • A. L. Tulupyev


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.


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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. Nilsson, Jr., “Probabilistic logic,” Artif. Intell. 47, 71–87 (1986).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    V. I. Gorodetskii, “Algebraic Bayesian networks — New paradigm of expert systems,” in Jubilee Collection of Works of Institutes of the Department of Informatics, Computer Science and Automation of RAS (Otd. Inf., Vychisl. Tekh. i Avtom. Ross. Akad. Nauk, Moscow, 1993), Vol. 2, pp. 120–141 [in Russian].Google Scholar
  3. 3.
    V. I. Gorodetskii and A. L. Tulup’ev, “Generating consistent knowledge bases with uncertainty,” J. Comput. Syst. Sci. Int. 36, 683–691 (1997).zbMATHGoogle Scholar
  4. 4.
    G. Cosma, D. Brown, M. Archer, M. Khan, and A. G. Pockley, “A survey on computational intelligence approaches for predictive modeling in prostate cancer,” Expert Syst. Appl. 70, 1–19 (2017).CrossRefGoogle Scholar
  5. 5.
    M. W. L. Moreira, J. J. P. C. Rodrigues, A. M. B. Oliveira, R. F. Ramos, and K. Saleem, “A preeclampsia diagnosis approach using Bayesian networks,” in Proc. IEEE Int. Conf. on Communications (ICC), Kuala Lumpur, Malaysia, May 23–27, 2016 (IEEE, Piscataway, NJ, 2016).Google Scholar
  6. 6.
    C. Tang, Y. Yi, Z. Yang, and J. Sun, “Risk analysis of emergent water pollution accidents based on a Bayesian Network,” J. Environ. Manage. 165, 199–205 (2016).CrossRefGoogle Scholar
  7. 7.
    S. Barua, X. Gao, H. Pasman, and M. S. Mannan, “Bayesian network based dynamic operational risk assessment,” J. Loss Prev. Process Ind. 41, 399–410 (2016).CrossRefGoogle Scholar
  8. 8.
    J.-L. Molina, S. Zazo, P. Rodríguez-González, and D. González-Aguilera, “Innovative analysis of runoff temporal behavior through Bayesian networks,” Water 8, 484 (2016).CrossRefGoogle Scholar
  9. 9.
    H. M. Nemati, A. Sant’Anna, and S. Nowaczyk, “Bayesian Network representation of meaningful patterns in electricity distribution grids,” in Proc. IEEE Int. Energy Conf., Leuven, Belgium, Apr. 4–8, 2016 (IEEE, Piscataway, NJ, 2016).Google Scholar
  10. 10.
    P. Gehl and D. D’Ayala, “Development of Bayesian Networks for the multi-hazard fragility assessment of bridge systems,” Struct. Saf. 60, 37–46 (2016).CrossRefGoogle Scholar
  11. 11.
    L. Zhang, X. Wu, Y. Qin, M. J. Skibniewski, and W. Liu, “Towards a fuzzy Bayesian Network based approach for safety risk analysis of tunnel-induced pipeline damage,” Risk Anal. 36, 278–301 (2016).CrossRefGoogle Scholar
  12. 12.
    B. Ojeme and A. Mbogho, “Predictive strength of Bayesian networks for diagnosis of depressive disorders”, in Proc. 8th KES Int. Conf. on Intelligent Decision Technologies (KES-IDT 2016), Puerto de la Cruz, Spain, June 15–17, 2016 (Springer-Verlag, Cham, Switzerland, 2016), pp. 373–382.Google Scholar
  13. 13.
    N. V. Hovanov, Analysis and Synthesis of Indicators with Information Shortage (S.-Peterb. Gos. Univ., St. Petersburg, 1996) [in Russian].Google Scholar
  14. 14.
    S. Lei, K. Mao, L. Li, W. Xiao, and B. Li, “Direct method for second-order sensitivity analysis of modal assurance criterion,” Mech. Syst. Signal Process. 76, 441–454 (2016).CrossRefGoogle Scholar
  15. 15.
    F. Pianosi, K. Beven, J. Freer, J. W. Hall, J. Rougier, D. B. Stephenson, and T. Wagener, “Sensitivity analysis of environmental models: A systematic review with practical workflow,” Environ. Modell. Software 79, 214–232 (2016).CrossRefGoogle Scholar
  16. 16.
    A. L. Tulupyev, A. V. Sirotkin, and A. A. Zolotin, “Matrix equations for normalizing factors in local a posteriori inference of truth estimates in algebraic Bayesian networks,” Vestn. St. Petersburg Univ.: Math. 48, 168–174 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    A. A. Zolotin, A. L. Tulupyev, and A. V. Sirotkin, “Matrix-vector algorithms of local posteriori inference in algebraic bayesian networks on quanta propositions,” Nauchno-Tekh. Vestn. Inf. Tekhnol., Mekh. Opt. 15, 676–684 (2015).CrossRefzbMATHGoogle Scholar
  18. 18.
    A. L. Tulupyev, Bayesian Networks: Probabilistic-Logic Inference in Cycles (S.-Peterb. Gos. Univ., St. Petersburg, 2008) [in Russian].Google Scholar
  19. 19.
    A. L. Tulupyev, A. V. Sirotkin, and S. I. Nikolenko, Bayesian Belief Networks: Probabilistic-Logic Inference in Acyclic Directed Graphs (S.-Peterb. Gos. Univ., St. Petersburg, 2009) [in Russian].Google Scholar
  20. 20.
    A. L. Tulupyev, S. I. Nikolenko, and A. V. Sirotkin, Bayesian Networks: Probabilistic-Logic Approach (Nauka, St. Petersburg, 2006) [in Russian].Google Scholar
  21. 21.
    A. L. Tulupyev and A. V. Sirotkin, “Matrix-vector equations for local probabilistic-logic inference in algebraic Bayesian networks,” Vestn. S.-Peterb. Univ., Ser. 1: Mat., Mekh., Astron., No. 3, 63–72 (2012).Google Scholar
  22. 22.
    A. L. Tulupyev and A. V. Sirotkin, “Sensitivity of the results of local a priori and local posteriori inference in algebraic Bayesian networks,” in Proc. Scientific Session of NRNU MEPhI–2010, Moscow, Jan. 25–31, 2010 (NIYaU MIFI, Moscow, 2010), p. 75.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.St. Petersburg Institute for Informatics and AutomationRussian Academy of SciencesSt. PetersburgRussia

Personalised recommendations