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Ignacio Montes

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4 papers

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ISIPTA Conference 2025 Conference Paper

Distorting lower probabilities using common distortion models

David Nieto-Barba
Ignacio Montes
Enrique Miranda

Distortion or neighbourhood models are useful tools in the imprecise probability theory allowing to robustify a probabilistic model by considering a neighbourhood around a given probability measure. In this work, we tackle the more general problem of distorting a lower probability. This problem can be interesting when we believe that a given lower probability is too precise, or in coalitional game theory when the set of solutions is empty. Our main purpose is to investigate how the linear vacuous and pari mutuel models can be defined for the distortion of lower probabilities, and for this aim we address the problem in a more general manner: we extend the vertical barrier models, which include the linear vacuous and pari mutuel models, and investigate the properties they satisfy.

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ISIPTA Conference 2025 Conference Paper

On the closure of aggregation rules for imprecise probabilities

Enrique Miranda
Ignacio Montes

We consider the problem of aggregating a number of imprecise probability models into a joint one, and compare four aggregation rules: conjunction, disjunction, mixture and Pareto. We investigate for which particular cases of imprecise probability models these operators are closed, meaning that the output belongs to the same family as the inputs. Specifically, we analyse this problem for comparative probability models, $2$-monotone capacities, probability intervals, belief functions, p-boxes and minitive measures.

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ISIPTA Conference 2017 Conference Paper

A Study of the Pari-Mutuel Model from the Point of View of Imprecise Probabilities

Ignacio Montes
Enrique Miranda
Sébastien Destercke

The Pari-Mutuel model is a distortion model that has its origin in horse racing. Since then, it has been applied in many different fields, such as finance or risk analysis. In this paper we investigate the properties of the Pari-Mutuel model within the framework of Imprecise Probabilities. Since a Pari-Mutuel model induces (2-monotone) coherent lower and upper probabilities, we investigate its connections with other relevant models within this theory, such as probability intervals and belief functions. We also determine the number of extreme points of the credal set induced by the Pari-Mutuel model and study how to combine the information given by multiple Pari-Mutuel models.

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ISIPTA Conference 2017 Conference Paper

Game Solutions, Probability Transformations and the Core

Enrique Miranda
Ignacio Montes

We investigate the role of some game solutions, such the Shapley and the Banzhaf values, as probability transformations of lower probabilities. The first one coincides with the pignistic transformation proposed in the Transferable Belief Model the second one is not efficient in general, leading us to propose a normalized version. We consider a number of particular cases of lower probabilities: minitive measures, coherent lower probabilities, as well as the lower probabilities induced by comparative or distorsion models. For them, we provide some alternative expressions of the transformations and study when they belong to the core of the lower probability.

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