Uncertainty measures on probability intervals from the imprecise Dirichlet model

Abstract

When we use a mathematical model to represent information, we can obtain a closed and convex set of probability distributions, also called a credal set. This type of representation involves two types of uncertainty called conflict (or randomness) and non-specificity, respectively. The imprecise Dirichlet model (IDM) allows us to carry out inference about the probability distribution of a categorical variable obtaining a set of a special type of credal set (probability intervals). In this paper, we shall present tools for obtaining the uncertainty functions on probability intervals obtained with the IDM, which can enable these functions in any application of this model to be calculated.

Keywords:

• Imprecise probabilities
• Credal sets
• Uncertainty
• Entropy
• Conflict
• Imprecise Dirichlet model

Acknowledgement

This work has been supported by the Spanish Ministry of Science and Technology under the Algra project (TIN 2004-06204-C03-02).