Learning from multinomial data: a nonparametric predictive alternative to the Imprecise Dirichlet Model

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 [16], 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.