Uncertainty-based information measures on the approximate non-parametric predictive inference model

The Non-Parametric Predictive Inference Model for Multinomial Data (NPI-M) is an imprecise probabilities model used to represent the available information about a categorical variable. It presents some advantages over another imprecise probabilities model frequently used in the literature called Imprecise Dirichlet Model (IDM), which assumes previous knowledge about the data through a parameter. The Approximate Non-Parametric Predictive Inference Model for Multinomial Data (A-NPI-M) is a model similar to the NPI-M that can be expressed by reachable sets of probability intervals, is easier to manage, and is non-parametric. As a novelty, in this work, we analyze the main properties of A-NPI-M credal sets, comparing them with the properties of credal sets associated with the IDM. Moreover, we present procedures to calculate the most important uncertainty measures on A-NPI-M credal sets. Those procedures represent useful tools to make the A-NPI-M very suitable to be used in practical applications.