A new model for learning from multinomial data has recently been developed, giving predictive inferences in the form of lower and upper probabilities for a future observation. Apart from the past observations, no information on the sample space is assumed, so explicitly no assumptions are made on the number of possible categories. In this paper, we briefly present the general lower and upper probabilities corresponding to this model, and illustrate their properties via two examples taken from Walley's paper which introduced the imprecise Dirichlet model (IDM). As our approach is nonparametric, its applicability is more restricted. However, our inferences do not suffer from some disadvantages of the IDM.
Keywords. Imprecise Dirichlet model, imprecise probabilities, interval probability, multinomial data, nonparametric predictive inference, probability wheel
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Department of Mathematical Sciences
Science Laboratories, South Road
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Department of Statistics
University of Munich