Miscelaneous work
E. Miranda,
G. de Cooman. Coherence and
independence in non-linear spaces.
We extend
some of the concepts from the behavioural theory of imprecise probabilities,
such as weak and strong coherence, to non-linear spaces of gambles, and we
study the relations between them. Then, we see some simplifications under the
assumption of epistemic independence of experiments and we study the
independent natural extension from given marginals.
E. Miranda, I. Montes. Centroids of credal sets: a comparative study.
The problem of eliciting a single probability from a closed and convex set of probability measures is interesting in a number of elds: in coalitional game theory for selecting a fair way of splitting the wealth between the players, in the transferable belief model from evidence theory or for transforming a second order into a rst order model. In this paper, we study this problem when the goal is to determine the centroid of a credal set, and we compare four approaches: the Shapley value, the average of the extreme points, the incenter with respect to the total variation distance between probability measures and the limit of a procedure of uniform contraction. We show that these four centroids do not coincide in general, we give some su cient conditions for their equality, and we analyse their axiomatic properties. Finally, we also discuss how to de ne a notion of centrality measure indicating the degree of centrality of a probability measure in a credal set.
Pablo Ramsés Alonso-Martín, Ignacio Montes, Enrique Miranda. Distortion models for estimating human error probabilities.
Human Reliability Analysis aims at identifying, quantifying and proposing solutions to human factors causing hazardous consequences. Quantifying the influence of the human factors gives rise to human error probabilities, whose estimation is a cumbersome problem. Since these human factors are usually related to other organisational or technological factors, it has been proposed to apply probabilistic graphical models, such as Bayesian or credal networks. However, these can be problematic when conditional probabilities on missing data are involved. While the solutions proposed so far combine frequentist and subjective approaches and are in general not robust to small modifications in the dataset, in this paper we propose an alternative based on distortion models, which are a type of imprecise probabilities. We perform a comparative analysis, showing that our proposal is consistent with the previous studies while giving rise to robust estimations.