Enrique Miranda and Ignacio Montes attended the conference, where they presented the following works:

• Análisis del efecto del redondeo en tests de normalidad mediante el uso de conjuntos aleatorios, by Marina Iturrate-Bobes, Ignacio Montes and Raúl Pérez-Fernández.
• Comparación de criterios de optimalidad para probabilidades imprecisas, by Nicolás Carrizosa, Ignacio Montes and Enrique Miranda.

The conference was held at the University of Santiago de Compostela and brought together around 600 participants, with four renowned plenary speakers: Peter Bühlmann, Irène Gijbels, Jiming Jiang and José Fernando Oliveira. In addition to the extensive scientific programme, we also had the opportunity to enjoy a fantastic social programme, including a welcome cocktail in the city centre of Santiago, a boat trip along the Ría de Arousa, and a wonderful gala dinner at the Pazo de Vista Alegre.

During the SEIO Society meeting, it was announced that SEIO 2028 will take place in Zaragoza, while SEIO 2029 will be held in Barcelona. It is always a pleasure to attend conferences organised by SEIO, where we can not only share our scientific advances but also meet friends and colleagues from different universities. We are therefore already looking forward to the next SEIO conference in Zaragoza!

Finally, we would like to congratulate our friend and colleague Juan Baz, from the UNIMODE research group at the University of Oviedo, who was awarded the prestigious Ramiro Melendreras Award during the closing ceremony. Congratulations, Juan!

On the definition of median for a random interval

has been accepted for publication in Information Sciences.

This paper, written by Olaya González-Campos, Raúl Pérez-Fernández and Enrique Miranda, addresses the problem of extending the classical notion of median to set-valued observations in the context of random intervals under the epistemic interpretation. We model imprecise data arising from absolute measurement error, relative measurement error, and data rounding, providing a solid theoretical foundation for location statistics when precise observations are unavailable.

In particular, in this contribution we introduce four distinct notions of median for a random interval: the median, the extended median, the weak median, and the n-empirical median. For each of these constructs, we study their main mathematical properties and provide explicit characterizations when the lower and upper bounds of the interval are comonotone. Finally, we show how all four definitions extend naturally to general p-order quantiles and their linear combinations.

The conference program consisted of 14 parallel sessions and four plenary talks. Among the plenary speakers, we had the opportunity to listen to Marco Zaffalon, a frequent collaborator of Enrique Miranda, and Ángeles Gil, our colleague at the University of Oviedo, who summarised her long career devoted to the analysis of fuzzy data.

The members of IMAGINE organized two special sessions: one on “Aggregation Theory in Non-Traditional Contexts”, comprising three presentations, and another on “Theoretical and Applied Aspects of Imprecise Probabilities”, comprising nine presentations.

At the conference, we presented seven contributions. On Monday, June 15, during the special session on aggregation theory, Marina Iturrate-Bobes and Raúl Pérez-Fernández presented the papers “Two-sample goodness-of-fit tests to a location-scale family using OWA-based skewness coefficients” and “Asymptotic confidence intervals for a skewness parameter using OWA functions”.

On Tuesday, June 16, during the special session on imprecise probabilities, Darío Tagarro, Nicolás Carrizosa, Enrique Miranda and Ignacio Montes presented four papers: “An order-theoretic study of the credal sets generated by comparative probabilities”, “Decision making with generalized distortion models”, “Weighted Total Variation distances for contextual robustification”, and “On the commutativity of the aggregation of capacities and the natural extension to gambles”.

Finally, on Wednesday, June 17, David Nieto-Barba presented his paper “On the specific commutativity with Bayesian conditioning of systematic aggregation rules for probability measures”.

On Thursday, June 18, we enjoyed a guided tour through the city center of Rome, visiting iconic places such as the Trevi Fountain and the Pantheon. Afterwards, we attended a wonderful gala dinner. During the dinner, the traditional awards were given, and Nicolás Carrizosa received the IJAR Best Student Paper Award.

Overall, during these days we enjoyed both the scientific and social aspects of the conference, and we will keep many fond memories of it. Last but not least, we would like to congratulate the organising committee for all the work they put into making this conference such a success. See you in Warsaw at the IPMU 2028 conference!

On the closedness of imprecise probability models under aggregation

has been accepted for publication in the International Journal of General Systems.

This paper, authored by Enrique Miranda and Ignacio Montes, explores the aggregation of particular families of imprecise probability models, and continues our line of research on the aggregation of imprecise probability models, initiated with our previous publication “A Comparative Analysis of Aggregation Rules for Coherent Lower Previsions” and the conference paper “On the commutativity of the aggregation of coherent lower probabilities and the natural extension to gambles”.

In particular, in this contribution we consider six different models, namely comparative probabilities (Section 4), 2-monotone capacities (Section 5), probability intervals (Section 6), belief functions (Section 7), minitive measures (Section 8), and p-boxes (Section 9). For each of these models, we analyse whether several aggregation rules (conjunction, disjunction, convex mixtures, Pareto, conjunction–disjunction, and maximal consistent subsets rules) are closed within the family, in the sense that if the initial models to be aggregated belong to one of these families, the resulting model also belongs to the same family.

We have submitted two papers, and both of them have been accepted for presentation:

1. Análisis del efecto del redondeo en tests de normalidad mediante el uso de conjuntos aleatorios, by Marina Iturrate-Bobes, Ignacio Montes and Raúl Pérez-Fernández.
2. Comparación de criterios de optimalidad para probabilidades imprecisas, by Nicolás Carrizosa, Ignacio Montes and Enrique Miranda.

We are looking forward to attending this conference and to having the opportunity once again to meet members of the Spanish statistical and operations research community.

We have submitted four papers, all of which have been accepted for presentation:

1. Testing convex-ordering dominance via OWA-based skewness coefficients, by Marina Iturrate-Bobes, Ignacio Montes and Raúl Pérez-Fernández.
2. Skewness coefficients for rounded data, by Marina Iturrate-Bobes, Ignacio Montes and Raúl Pérez-Fernández.
3. The Imprecise Kolmogorov Model for robustifying p-boxes, by David Nieto-Barba, Ignacio Montes and Enrique Miranda.
4. Measuring incoherence for lower probabilities, by Juan Jesús Salamanca, Enrique Miranda and Ignacio Montes.

Moreover, we are organising the special session: Theoretical and applied aspects of imprecise probabilities (by Enrique Miranda and Raúl Pérez-Fernández).

Looking forward to seeing you in Lecce!

On the use of OWA functions for robustifying the Lilliefors test of goodness-of-fit to a location-scale family

has been accepted for publication in Fuzzy Sets and Systems.

The aim of this paper, authored by Marina Iturrate-Bobes, Raúl Pérez-Fernández and Bernard de Baets, is to construct a robust version of the Lilliefors normality test that is not affected by outliers.

To this end, Ordered Weighted Averaging (OWA) functions are used to bound the range in which the statistic is computed, as well as to provide robust estimates of the mean and standard deviation. Moreover, this robust version can be used to test goodness-of-fit to any distribution, not only the normal distribution. This is explored in Section 3, where an explicit formula for the statistic is provided. Section 4 presents an experimental study in which the role of each parameter is analysed and the potential of the test in the presence of outliers is demonstrated.

We have submitted eight papers, all of which have been accepted for presentation:

1. Two-sample goodness-of-fit tests to a location-scale family using OWA-based skewness coefficients, by Marina Iturrate-Bobes, Ignacio Montes and Raúl Pérez-Fernández.
2. Asymptotic confidence intervals for a skewness parameter by using OWA functions, by Marina Iturrate-Bobes, Ignacio Montes and Raúl Pérez-Fernández.
3. Weighted Total Variation distances for contextual robustification, by David Nieto-Barba, Enrique Miranda and Sebastién Destercke.
4. An order-theoretic study of the credal sets generated by comparative probabilities, by Darío Tagarro, Enrique Miranda and Raúl Pérez-Fernández.
5. On the commutativity of the aggregation of capacities and the natural extension to gambles, by Ignacio Montes and Enrique Miranda.
6. Decision making with generalised distortion models, by Nicolás Carrizosa, Ignacio Montes and Enrique Miranda.
7. On the specific commutativity with Bayesian conditioning of systematic aggregation rules for probability measures, by David Nieto-Barba and Sebastién Destercke.
8. Construction methods for uninorms on a specific family of bounded lattices, by Ánder Goñi, Raúl Pérez-Fernández and Marisol Gómez.

Moreover, we are organising two special sessions: Aggregation Theory in Non-Traditional Contexts (by Raúl Pérez-Fernández and Bernard de Baets) and Theoretical and Applied Aspects of Imprecise Probabilities (by David Nieto-Barba and Ignacio Montes). Last but not least, Nicolás Carrizosa has received an EUSFLAT grant to attend the conference.

Looking forward to seeing you in Rome!

Confidence intervals with imprecise data

has been accepted for publication in Statistical Papers.

This paper, written by Darío Tagarro, Raúl Pérez-Fernández and Enrique Miranda, addresses the problem of accounting for imprecision in the process of measuring a continuous variable in the context of confidence intervals for parameters of probability distributions.  We generalize the classical notion of confidence interval in the presence of imprecision by introducing the notions of inner and outer confidence interval, studying different properties of both mathematical constructs and providing their explicit expressions in five prominent cases in the field of Statistics.

After introducing in Section 2 some basic concepts on random sets, random intervals and confidence intervals, we give our definition of the inner and outer confidence intervals in Section 3. In Section 4 we present some properties related to their coverage and characterization. In particular, we derive an explicit expression of both constructs in terms of the extrema of the lower and upper bound functions of the confidence interval. Finally, we discuss in Section 5 five relevant examples of confidence intervals and provide the explicit formulae of the inner and outer confidence intervals under imprecision. For this aim, we have introduced the notions of quasivertex and 2-quasivertex, that have allowed us to simplify the optimization problem associated with the computation of the inner and outer intervals.

Neighbourhood models induced by the Euclidean distance and the Kullback-Leibler divergence

has been accepted for publication in Fuzzy Sets and Systems.

This paper, authored by Ignacio Montes, continues the research on distortion or neighbourhood models, a class of robust probabilistic models obtained by creating a neighbourhood of probability measures centred on a given initial probability, with a given radius and with respect to a distorting function used to compare probability measures. In particular, this paper investigates the imprecise probability models that arise when considering the Euclidean distance or the Kullback–Leibler divergence as the distorting function.

To this end, after introducing some preliminaries in Section 2, Section 3 is devoted to the distortion model determined by the Euclidean distance. A closed formula for the lower prevision associated with this model is obtained, and some interesting properties are presented. For example, while the lower prevision is not 2-monotone on gambles, it is 2-monotone on events.

Section 4 performs a similar study for the distortion model induced by the Kullback–Leibler divergence. Not surprisingly, this model is more difficult to handle from an analytical point of view. Nevertheless, it is possible to prove that, like the Euclidean model, it is 2-monotone on events but not on gambles.

Section 5 presents a comparison of the Euclidean and Kullback–Leibler models with some well-known distortion models, such as the linear vacuous model (also known as epsilon-contamination), the pari-mutuel model, the total variation model, and the constant odds ratio model. This comparative study shows that, at least from a practical point of view, the Euclidean and Kullback–Leibler models do not possess particularly attractive properties, even though their utility and interpretation as distortion models are unquestionable.