Nonparametric predictive inference (NPI) is a framework for statistical inference in the absence of prior knowledge. We present NPI for multinomial data with subcategories, motivated by the hierarchical structure of many multinomial data sets. We consider situations with known and with unknown numbers of subcategories, and present lower and upper probabilities for general events involving one future observation. We present properties of the model and an algorithm to derive an approximation to the maximum entropy distribution.
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