Multinomial nonparametric predictive inference with sub-categories

Nonparametric predictive inference (NPI) is a powerful tool for predictive inference under nearly complete prior ignorance. After summarizing our NPI approach for multinomial data, as presented in [8, 9], both for situations with and without known total number of possible categories, we illustrate how this approach can be generalized to deal with sub-categories, enabling consistent inferences at, different levels of detail for the specification of observations. This approach deals with main categories and sub-categories in a logical manner, directly based on the powerful probability wheel representation for multinomial data that is central to our method and that ensures strong internal consistency properties. Detailed theory for such inferences, enabling for example more layers of sub-categories as might occur in tree-like data base structures, has yet to be developed, but is conceptually straightforward and in line with the illustrations for more basic inferences presented in this paper.