Skip to main content

Non-Bayesian statistical decision making

  • Chapter

Part of the book series: Computational Imaging and Vision ((CIVI,volume 24))

Abstract

The enormous generality of the Bayesian approach has been emphasised in the first lecture several times. It follows from the fact that the problem formulation and some of its properties are valid for the diverse set structure of the observations X, states K, and decisions D. It is surely desirable to master the whole richness of Bayesian tasks, and not to identify it with a special case. We already know that the class of Bayesian tasks is more than minimisation of the probability of a wrong decision.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographical notes

  • Kuhn, H. and Tucker, A. (1950). Nonlinear programming. In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pages 481–492, Berkeley, Calif.

    Google Scholar 

  • Lehmann, E. (1959). Testing statistical hypotheses. John Willey, New York.

    MATH  Google Scholar 

  • Linnik, J. (1966). Statisticheskie zadachi s meshajushchimi parametrami; in Russian (Statistical tasks with intervening parameters). Nauka, Moskva.

    Google Scholar 

  • Neyman, J. (1962). Two breakthroughs in the theory of statistical decision making. Review de l’Inst. Intern. de Stat., 30 (1): 11–27.

    Article  MathSciNet  MATH  Google Scholar 

  • Neyman, J. and Pearson, E. (1928). On the use and interpretation of certain test criteria for purposes of statistical inference. Biometrica, 20A: 175–240.

    Google Scholar 

  • Neyman, J. and Pearson, E. (1933). On the problem of the most efficient tests of statistical hypotheses. Phil. Trans. Royal Soc. London, 231: 289–337.

    Google Scholar 

  • Schlesinger, M. (1979a). Dopolnitelnyje sledstvia teorii dvojstvennosti v nebayesovskich zadachach raspoznavania; in Russian (Additional consequences of the duality theory in non-Bayesian recognition tasks). In Raspoznavanie graficheskich i zvukovych signalov (Recognition of graphic and sound signals), pages 36–47, Kiev. Institut Kibernetiki AV USSR.

    Google Scholar 

  • Schlesinger, M. (1979b). Teoria dvojstvennosti v nebayesovskich zadachach raspoznavania; in Russian (Theory of duality in non-Bayesian recognition tasks). In Raspoznavanie graficheskich i zvukovych signalov (Recognition of graphic and sound signals), pages 21–35, Kiev. Institut Kibernetiki AV USSR.

    Google Scholar 

  • Wald, A. (1947). Sequential analysis. John Wiley, New York.

    MATH  Google Scholar 

  • Wald, A. (1950). Basic ideas of a general theory of statistical decision rules,. I. Proceedings of the International Congress of Mathematicians, volume I. Russian translation, A. Wald: Posledovatelnyj analiz, Gosudarstvenoe izdatelstvo fiziko-matematiceskoj literatury, Moskva 1960, paper in Appendix., pages 308–325.

    Google Scholar 

  • Wald, A. and Wolfowitz, J. (1948). Optimum character of the sequential ratio test. Ann. Math. Stat., 19 (3): 326–339.

    Article  MathSciNet  MATH  Google Scholar 

  • Zuchovickij, S. and Avdejeva, L. (1967). Linejnoje i vypukloje programmirovanije; in Russian (Linenar and convex programming). Nauka, Moskva.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Schlesinger, M.I., Hlaváč, V. (2002). Non-Bayesian statistical decision making. In: Ten Lectures on Statistical and Structural Pattern Recognition. Computational Imaging and Vision, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3217-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-3217-8_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6027-3

  • Online ISBN: 978-94-017-3217-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics