Skip to main content
Log in

Nonparametric Predictive Category Selection for Multinomial Data

  • Published:
Journal of Statistical Theory and Practice Aims and scope Submit manuscript

Abstract

A new method is presented for selecting a single category or the smallest subset of categories, based on observations from a multinomial data set, where the selection criterion is a minimally required lower probability that (at least) a specific number of future observations will belong to that category or subset of categories. The inferences about the future observations are made using an extension of Coolen and Augustin’s nonparametric predictive inference (NPI) model to a situation with multiple future observations.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Augustin T., Coolen F.P.A., 2004. Nonparametric predictive inference and interval probability. Journal of Statistical Planning and Inference, 124, 251–272.

    Article  MathSciNet  Google Scholar 

  • Bechhofer R., Santner T., Goldsman D., 1995. Design and Analysis of Experiments for Statistical Selection, Screening and Multiple Comparisons. Wiley, New York.

    Google Scholar 

  • Coolen F.P.A., 1998. Low structure imprecise predictive inference for Bayes’ problem. Statistics & Probability Letters, 36, 349–357.

    Article  MathSciNet  Google Scholar 

  • Coolen F.P.A., 2006. On nonparametric predictive inference and objective Bayesianism. Journal of Logic, Language and Information, 15, 21–47.

    Article  MathSciNet  Google Scholar 

  • Coolen F.P.A., Augustin T, 2005. Learning from multinomial data: a nonparametric predictive alternative to the Imprecise Dirichlet Model. ISIPTA’05: Proceedings of the Fourth International Symposium on Imprecise Probability Theory and Applications, Cozman F.G., Nau R., Seidenfeld T. (Editors), p. p–125.

    Google Scholar 

  • Coolen F.P.A., Augustin T., 2009. A nonparametric predictive alternative to the Imprecise Dirichlet Model: the case of a known number of categories. International Journal of Approximate Reasoning, 50, 217–230.

    Article  MathSciNet  Google Scholar 

  • Coolen F.P.A., Coolen-Schrijner P., 2006. Nonparametric predictive subset selection for proportions. Statistics & Probability Letters, 76, 1675–1684.

    Article  MathSciNet  Google Scholar 

  • Coolen F.P.A., Coolen-Schrijner P., 2007. Nonparametric predictive comparison of proportions. Journal of Statistical Planning and Inference, 137, 23–33.

    Article  MathSciNet  Google Scholar 

  • Coolen F.P.A., van der Laan P., 2001. Imprecise predictive selection based on low structure assumptions. Journal of Statistical Planning and Inference, 98, 259–277.

    Article  MathSciNet  Google Scholar 

  • Coolen-Schrijner P., Coolen F.P.A., Troffaes M.C.M., Augustin T., 2009. Special issue on imprecision in statistical theory and practice. Journal of Statistical Theory and Practice, 3, issue 1.

    Google Scholar 

  • Hill B.M., 1968. Posterior distribution of percentiles: Bayes’ theorem for sampling from a population. Journal of the American Statistical Association, 63, 677–691.

    MathSciNet  MATH  Google Scholar 

  • Maturi T.A., Coolen-Schrijner P., Coolen F.P.A., 2010. Nonparametric predictive inference for competing risks. Journal of Risk and Reliability, 224, 11–26.

    MATH  Google Scholar 

  • Walley P., 1991. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London.

    Book  Google Scholar 

  • Walley, P. 1996. Inferences from multinomial data: learning about a bag of marbles (with discussion). Journal of the Royal Statistical Society B, 58, 3–57.

    MathSciNet  MATH  Google Scholar 

  • Weichselberger K., 2000. The theory of interval-probability as a unifying concept for uncertainty. International Journal of Approximate Reasoning, 24, 149–170.

    Article  MathSciNet  Google Scholar 

  • Weichselberger K., 2001. Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung I. Intervallwahrscheinlichkeit als umfassendes Konzept. Physika, Heidelberg, Germany.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rebecca M. Baker.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baker, R.M., Coolen, F.P.A. Nonparametric Predictive Category Selection for Multinomial Data. J Stat Theory Pract 4, 509–526 (2010). https://doi.org/10.1080/15598608.2010.10412000

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1080/15598608.2010.10412000

AMS Subject Classification

Key-words

Navigation