A nonparametric predictive alternative to the Imprecise Dirichlet Model: The case of a known number of categories

Authors:
F. P. A. Coolen;T. Augustin
Affiliations:
Durham University, Department of Mathematical Sciences, Science Laboratories, Durham DH1 3LE, UK;Ludwig-Maximilians University, Department of Statistics, Ludwigstr. 33, D-80539 Munich, Germany
Venue:
International Journal of Approximate Reasoning
Year:
2009

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Abstract

Nonparametric predictive inference (NPI) is a general methodology to learn from data in the absence of prior knowledge and without adding unjustified assumptions. This paper develops NPI for multinomial data when the total number of possible categories for the data is known. We present the upper and lower probabilities for events involving the next observation and several of their properties. We also comment on differences between this NPI approach and corresponding inferences based on Walley's Imprecise Dirichlet Model.