Measurement Techniques

, Volume 48, Issue 9, pp 894–900 | Cite as

Three Types of Mathematical Uncertainty Models

  • N. V. Khovanov


Mathematical models have been constructed for three types of uncertainty (interval, stochastic, and Bayesian), and the application of these models is discussed for describing measurements in the presence of unmonitored fluctuations leading to ambiguities in the results.

Key words

measurement uncertainty interval analysis Bayesian uncertainty model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. Knight, Risk, Uncertainty, and Profit, Houghton Mifflin Co., Boston, MA, USA (1921).Google Scholar
  2. 2.
    N. V. Khovanov, Parameter Analysis and Synthesis with Information Deficiency [in Russian], SPbGU, St. Petersburg (1996).Google Scholar
  3. 3.
    N. V. Khovanov, Mathematical Models for Risk and Uncertainty [in Russian], SPbGU, St. Petersburg (1998).Google Scholar
  4. 4.
    N. V. Khovanov, Izmer. Tekh., No. 9, 15 (2003).Google Scholar
  5. 5.
    P. Pao, Linear Statistical Methods and Their Applications [Russian translation], Nauka, Moscow (1968).Google Scholar
  6. 6.
    M. Nogueira and A. Nandigam, Reliable Computing, 4, 389 (1998).CrossRefMathSciNetGoogle Scholar
  7. 7.
    D. Dennis, V. Kreinovich, and S. Rump, ibid., p. 191.Google Scholar
  8. 8.
    G. Alefeld and J. Herzberger, Introduction to Interval Calculus [Russian translation], Mir, Moscow (1987).Google Scholar
  9. 9.
    V. M. Bradis, Encyclopedia of Elementary Mathematics, Volume 1, Arithmetic [in Russian], GITTL, Moscow and Leningrad (1951), p. 388.Google Scholar
  10. 10.
    Yu. B. Germeier, Introduction to Operational Research Theory [in Russian], Nauka, Moscow (1971).Google Scholar
  11. 11.
    I. V. Dunin-Barkovskii and N. V. Smirnov, Probability Theory and Mathematical Statistics in Engineering [in Russian], GITTL, Moscow (1955).Google Scholar
  12. 12.
    A. N. Krylov, Lectures on Approximate Calculations [in Russian], GITTL, Moscow (1954).Google Scholar
  13. 13.
    L. E. Maistrov, Probability Theory: A Historical Outline [in Russian], Nauka, Moscow (1967).Google Scholar
  14. 14.
    M. Kendall and A. Stuart, Distribution Theory [Russian translation], Nauka, Moscow (1966).Google Scholar
  15. 15.
    B. V. Gnedenko, Textbook of Probability Theory [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
  16. 16.
    Guide to the Expression of Uncertainty in Measurement [in Russian], VNIIM, St. Petersburg (1999).Google Scholar
  17. 17.
    Guide to the Expression of Uncertainty in Measurement, ISO, Geneva (1993).Google Scholar
  18. 18.
    A. Zelner, Bayesian Methods in Econometrics [Russian translation], Statistika, Moscow (1980).Google Scholar
  19. 19.
    T. Bayes, Biometrika, 5, Pt. 3–4, 296 (1958); reproduced from Phil. Trans. Royal Soc., 53 (1763).Google Scholar
  20. 20.
    E. Jaynes, Foundations of Probability Theory and Statistical Mechanics [in Russian], Springer, New York (1967).Google Scholar
  21. 21.
    A. Shimony, Synthese, 63, 35 (1985).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • N. V. Khovanov

There are no affiliations available

Personalised recommendations