Skip to main content
SpringerLink
Log in

Bayesian decision criteria in the presence of noises under quadratic and absolute value loss functions

  • Article
  • Published:
Statistical Papers Aims and scope Submit manuscript

Summary

Misclassifications, or noises, in the sampling stage of a Bayesian scheme can seriously affect the values of decision criteria such as the Bayes Risk and the Expected Value of Sample Information. This problem does not seem to be much addressed in the existing literature. In this article, using an approach based on hypergeometric functions and numerical computation, we study the effects of these noises under the two most important loss functions: the quadratic and the absolute value. A numerical example illustrates these effects in a representative case, using both loss functions, and provides additional insights into the general problem.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Altman, D.G.,Practical Statistics for Medical research, Chapman and Hall/CRC, New York, 1999.

    Google Scholar 

  • Exton, H.,Multiple Hypergeometric Functions and Applications, Chichester-Ellis Howard, London, 1976.

    MATH  Google Scholar 

  • French, S. and Rios Insua, D.,Statistical Decision Theory, Arnold, London, 2000.

    Google Scholar 

  • Gaba, A. and Winkler, R.L., Implications of Errors in Survey Data: a Bayesian Model,Management Science, 38, 1992, 913–925.

    Article  MATH  Google Scholar 

  • Gaba, A. and Winkler, R.L., The Impact of Testing Errors on Value of Information: a Quality-Control Example,Journal of Risk and Uncertainty, 10, 1995, 5–13.

    Article  MATH  Google Scholar 

  • Hilton, R.W., The Determinants of Information Value: Synthesizing Some General Results,Management Science, 27, 1981, 57–64.

    Google Scholar 

  • Johnson, N.J. and Kotz, S., Errors in Inspection and Grading: Distributional Aspects of Screening and Hierarchical Screening,Commun. in Stat-Theory-Meth, 1982, 1997–2016.

  • Pham-Gia, T. and Turkhan, N., Sample Size Determination in Bayesian Analysis,The Statistician, 41, 389–398, 1992a.

    Article  Google Scholar 

  • Pham-Gia, T. and Turkhan, N., Information Loss in a Noisy Dichotomous Sampling Process,Commun. Statist.-Theory Meth., 21(7), 2000–2018, 1992b.

    Google Scholar 

  • Pham-Gia, T., Duong, Q. and Turkhan, N., Using the Mean Absolute Deviation to Determine the Prior Distribution.Stat. and Prob. Letters, 13, 373–381, 1992c.

    Article  MATH  Google Scholar 

  • Pham-Gia, T. and Tranloc, H., The Mean Absolute Deviations.Mathl and Computer Modelling, 34, 2001, 921–936.

    Article  MATH  Google Scholar 

  • Pham-Gia, T., Turkhan, N. and Bekker, A., An L1-Approach in the Bayesian Analysis of the mixing proportion,the Scandinavian Journ. of Stat., 2002, submitted.

  • Rahali, B. and Foote, B.L., An Approach to Compensate for Uncertainty in Knowledge of Inspector Error,Journ. of Quality Technology, 14, 1982, 190–195.

    Google Scholar 

  • Rahme, E., Joseph, L. and Gyorkos, T.W., Bayesian Sample Size determination for Estimating Binomial Parameters from Data Subject to Misclassification.Appl. Statist., 49, 119–128, 2000.

    MATH  MathSciNet  Google Scholar 

  • Unnikhrishnan, N.K. and Kunte, S., Bayesian Analysis for Randomized Response Models.Sankhya: the Indian Journal of Statistics, 1999, 61, series B, 422–432.

    Google Scholar 

  • Winkler, R.L., Information Loss in Noisy and Dependent Processes, in: J.M. Bernardo, M.H. de Groot, D.V. Lindley and A.F.M. Smith (ed.),Bayesian Statistics 2, 559–570, Elsevier Science Publishers, North-Holland, N.Y., 1985.

    Google Scholar 

  • Winkler, R.L. and Gaba, A., Inference with Imperfect Sampling from a Bernoulli Process, p. 303–317, inBayesian and Likelihood Methods in Statistics and Economics, S. Geisser, J.S. Hodges, S.J. Press and A. Zellner, Ed., Elsevier Science Publishers B.V., 1990, Amsterdam.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Moncton, (Canada)

    T. Pham-Gia & N. Turkhan

Authors
  1. T. Pham-Gia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Turkhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research partially supported by NSERC grant A 9249 (Canada) and FICU Grant 2000/pas/13. The authors wish to thank colleagues at the University of Alberta in Edmonton, Canada, for very stimulating discussions, and an anonymous referee for drawing their attention to three relevant references that have enriched the content of this final version.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pham-Gia, T., Turkhan, N. Bayesian decision criteria in the presence of noises under quadratic and absolute value loss functions. Statistical Papers 46, 247–266 (2005). https://doi.org/10.1007/BF02762970

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02762970

Keywords and Phrases

AMS Classification

Search

Navigation