Calculating Uncertainty Intervals From Conditional Convex Sets of Probabilities

TL;DR

This paper explores methods to convert possibility distributions derived from convex sets of probabilities into uncertainty intervals using Sugeno and Choquet integrals, enhancing the interpretation of conditioned probabilistic information.

Contribution

It introduces and compares new techniques for transforming possibility distributions into probability intervals based on integrals, advancing the analysis of conditioned convex probability sets.

Findings

Sugeno and Choquet integrals produce different interval estimates.

The methods are illustrated through selected examples.

Transformations improve understanding of conditioned probabilistic data.

Abstract

In Moral, Campos (1991) and Cano, Moral, Verdegay-Lopez (1991) a new method of conditioning convex sets of probabilities has been proposed. The result of it is a convex set of non-necessarily normalized probability distributions. The normalizing factor of each probability distribution is interpreted as the possibility assigned to it by the conditioning information. From this, it is deduced that the natural value for the conditional probability of an event is a possibility distribution. The aim of this paper is to study methods of transforming this possibility distribution into a probability (or uncertainty) interval. These methods will be based on the use of Sugeno and Choquet integrals. Their behaviour will be compared in basis to some selected examples.