Jensen's and Cantelli's Inequalities with Imprecise Previsions

Autor: Pelessoni, Renato, Vicig, Paolo

We investigate how basic probability inequalities can be extended to an imprecise framework, where (precise) probabilities and expectations are replaced by imprecise probabilities and lower/upper previsions. We focus on inequalities giving informatio

Externí odkaz: http://arxiv.org/abs/2211.01503

Dilation Properties of Coherent Nearly-Linear Models

Autor: Pelessoni, Renato, Vicig, Paolo

Publikováno v: International Journal of Approximate Reasoning, 140, 211-231, January 2022

Dilation is a puzzling phenomenon within Imprecise Probability theory: when it obtains, our uncertainty evaluation on event $A$ is vaguer after conditioning $A$ on $B$, whatever is event $B$ in a given partition $\mathcal{B}$. In this paper we invest

Externí odkaz: http://arxiv.org/abs/2111.12811

Nearly-Linear uncertainty measures

Autor: Corsato, Chiara, Pelessoni, Renato, Vicig, Paolo

Publikováno v: International Journal of Approximate Reasoning, 114, pp. 1-28, November 2019

Several easy to understand and computationally tractable imprecise probability models, like the Pari-Mutuel model, are derived from a given probability measure P_0. In this paper we investigate a family of such models, called Nearly-Linear (NL). They

Externí odkaz: http://arxiv.org/abs/1908.11303

Weakly Consistent Extensions of Lower Previsions

Autor: Pelessoni, Renato, Vicig, Paolo

Publikováno v: Renato Pelessoni, Paolo Vicig, Weakly Consistent Extensions of Lower Previsions, Fuzzy Sets and Systems, vol. 328, 1 December 2017, pages 83-106

Several consistency notions are available for a lower prevision P assessed on a set D of gambles (bounded random variables), ranging from the well known coherence to convexity and to the recently introduced 2-coherence and 2-convexity. In all these i

Externí odkaz: http://arxiv.org/abs/1803.09940

2-coherent and 2-convex Conditional Lower Previsions

Autor: Pelessoni, Renato, Vicig, Paolo

Publikováno v: International Journal of Approximate Reasoning, vol. 77, October 2016, pages 66-86

In this paper we explore relaxations of (Williams) coherent and convex conditional previsions that form the families of $n$-coherent and $n$-convex conditional previsions, at the varying of $n$. We investigate which such previsions are the most gener

Externí odkaz: http://arxiv.org/abs/1606.06043