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.
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References
Augustin T., Coolen F.P.A., 2004. Nonparametric predictive inference and interval probability. Journal of Statistical Planning and Inference, 124, 251–272.
Bechhofer R., Santner T., Goldsman D., 1995. Design and Analysis of Experiments for Statistical Selection, Screening and Multiple Comparisons. Wiley, New York.
Coolen F.P.A., 1998. Low structure imprecise predictive inference for Bayes’ problem. Statistics & Probability Letters, 36, 349–357.
Coolen F.P.A., 2006. On nonparametric predictive inference and objective Bayesianism. Journal of Logic, Language and Information, 15, 21–47.
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.
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.
Coolen F.P.A., Coolen-Schrijner P., 2006. Nonparametric predictive subset selection for proportions. Statistics & Probability Letters, 76, 1675–1684.
Coolen F.P.A., Coolen-Schrijner P., 2007. Nonparametric predictive comparison of proportions. Journal of Statistical Planning and Inference, 137, 23–33.
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.
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.
Hill B.M., 1968. Posterior distribution of percentiles: Bayes’ theorem for sampling from a population. Journal of the American Statistical Association, 63, 677–691.
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.
Walley P., 1991. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London.
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.
Weichselberger K., 2000. The theory of interval-probability as a unifying concept for uncertainty. International Journal of Approximate Reasoning, 24, 149–170.
Weichselberger K., 2001. Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung I. Intervallwahrscheinlichkeit als umfassendes Konzept. Physika, Heidelberg, Germany.
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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
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DOI: https://doi.org/10.1080/15598608.2010.10412000