Uncertainty, Imprecise Probabilities and Interval Capacity Measures on a Product Space
Statistics Theory
2024-04-25 v1 Methodology
Statistics Theory
Abstract
In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we introduced the concepts of weak complementation and interval probability measures associated with a family of random variables, which effectively capture the inherent uncertainty in any event. This paper conducts a comprehensive analysis of these concepts within a specific probability space. Additionally, we elaborate on an updating rule for events, integrating essential concepts of statistical independence, dependence, and stochastic dominance.
Cite
@article{arxiv.2404.15484,
title = {Uncertainty, Imprecise Probabilities and Interval Capacity Measures on a Product Space},
author = {Marcello Basili and Luca Pratelli},
journal= {arXiv preprint arXiv:2404.15484},
year = {2024}
}