A brief history

Below is a summary of the group's history, made within the framework of the presentation to the CSIC Groups program at Udelar.

The Probability and Statistics group currently gathers researchers, undergraduate, and graduate students, distributed throughout the country at different university sites. It is made up of researchers from the Centro de Matemática (CMAT) of the School of Sciences, the Instituto de Matemática y Estadística «Rafael Laguardia» (IMERL) of the Faculty of Engineering, the Departmento de Métodos Cuantitativos (DMC) of the Faculty of Economics and Administration, the Departmento de Matemática y Estadística del Litoral (DMEL) as part of Cenur - Litoral Norte, as well as the Cenur Noreste - Tacuarembó. It also contacts colleagues from the Cenur Este and the Cenur Noreste - Rivera.

The foundational period and the democratic reconstruction

It has the vocation to be considered the heir to the research work initiated by Cesáreo Villegas on Bayesian Statistics in the early 1960s at the Instituto de Matemática y Estadística (IME, now IMERL) of the Faculty of Engineering, and later continued by Enrique Cabaña until his exile in Venezuela. The group resumed its post-dictatorship activities in 1986 with the Seminar on Probability and Statistics directed by Gonzalo Pérez Iribarren, Enrique Cabaña, Mario Wschebor, and Ricardo Fraiman, all four coming from exile. It has maintained uninterrupted activity in different venues and formats and obviously with variations in its integration.

An important characteristic of the group, instilled by its founders, was to consider probability and statistics as disciplines that should be cultivated jointly, following the French and Russian traditions, as opposed to the Saxon one.

The research topics of the group changed and expanded over time. The founding intention was to cultivate mathematical statistics with applications in engineering. The first work [1] was published by Villegas in 1961, followed by publications by Wschebor in 1965 ([2] corresponding to his studies in Hungary) and by Cabaña in 1966 [3]. Although the first publications are in statistics (particularly in Bayesian statistics by Villegas), later publications are devoted to probability and stochastic processes. For example, in 1970, Cabaña published a celebrated paper [4] on the problem of the vibrating string subjected to white noise, and in 1973 Wschebor published the solution of a problem on random intervals on the circle [5]. In the post-dictatorship period, Ricardo Fraiman consolidates a line of non-parametric statistics with the collaboration of Gonzalo Pérez Iribarren.

The third Congress of Probability and Mathematical Statistics (CLAPEM), organized in 1988 in Montevideo by Cabaña and Wschebor was a milestone in the consolidation of international links and brought the group closer to the first graduate students to study in the country. One of them was Gonzalo Perera, the first Ph.D. in mathematics in the country. He worked on his thesis on central limit theorems for multidimensional mixing processes under the supervision of Wschebor. The congress was marked by the participation of specialists from all over the world, among them, Prof. Albert Shiryaev, at that time president of the international society of probability and statistics called «Bernoulli Society», who was Ernesto Mordecki's doctoral tutor in Moscow.


[1] C. Villegas. Maximum likelihood estimation of a linear functional relationship. Ann. Math. Statist. 32 (1961), 1048–1062.

[2] P. Révész, M. Wschebor. On the statistical properties of the Walsh functions. Magyar Tud. Akad. Mat. Kutató Int. Közl. 9 (1965), 543–554.

[3] E.M. Cabaña. Stochastic integration in separable Hilbert spaces. Univ. Repúb. Fac. Ingen. Agrimens. Montevideo Publ. Inst. Mat. Estadíst. 4 (1966), 49–80.

[4] E.M. Cabaña. The vibrating string forced by white noise. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 15 (1970), 111–130.

[5] M. Wschebor. Sur le recouvrement du cercle par des ensembles placés au hasard. Israel J. Math. 15 (1973), 1–11.

The group at present

The group comprises 16 researchers with doctoral degrees and 9 students between undergraduate and graduate studies.

Among the most recent research topics are random geometry, inspired by the works of Shub and Smale, taken up by Mario Wschebor, and currently developed by Federico Dalmao and Diego Armentano (both under the advice of Wschebor in their Ph.D.s), and José Rafael León; The stochastic calculus and its applications, promoted by Ernesto Mordecki after his studies in Moscow, including applications in finance and engineering developed in the doctoral theses of Andrés Sosa and Laura Aspirot, respectively; The applications to telecommunications, promoted by Paola Bermolen after her Ph.D. in Telecom-Paris, which contains recent results on large deviations in Valeria Goicoechea's Ph.D. thesis; The biostatistics promoted by María Inés Fariello after her studies in Toulouse; The links between probability and analysis cultivated by Nicolás Frevenza after his studies in Buenos Aires are examples of the multiple lines of research in development. Concomitantly, work is being done on various problems of non-parametric statistics, functional data statistics, and set estimation, in which Alejandro Cholaquidis and Leonardo Moreno (both Ph.D. under the supervision of Ricardo Fraiman) are actively participating. Other topics in the area of statistics are supervised learning, with results obtained in the Ph.D. thesis of Mathias Bourel (supervised by Badih Ghattas and Ricardo Fraiman), and statistics in time series and applications, in particular for long memory processes, led by Juan Kalemkerian (Ph.D. in the group under the supervision of Enrique Cabaña).

The retirement of Enrique Cabaña (who continues in some group activities) and the death of Mario Wschebor in 2011 generated a challenge to the organizational continuity of the group. In this sense, a very important event for the academic life of the group was the arrival in 2017 of Prof. José Rafael León, of extensive scientific and university career in Venezuela and France and with intense previous collaboration with members of the group. In December 2022, a congress dedicated to commemorating the 70th anniversary of José Rafael León and the 60th anniversary of the French mathematician Marc Lavielle will be held in Montevideo. This event consolidates the long-standing cooperation between Uruguay, Venezuela, and France in Probability and Statistics.

Regional and international links

At the international level, the group's insertion and its members' work were very relevant for creating academic institutions at the Latin American level, starting with the Latin American section of the Bernoulli Society, founded by Enrique Cabaña and Mario Wschebor in Venezuela.

CLAPEM 2004 was held in Uruguay and was organized by the Latin American Region of the Bernoulli Society. It was a milestone in the group's life due to the event's relevance and the invited conferences. It also constituted one of the first approaches to Probability and Statistics for current members who were pursuing their bachelor's or master's degrees at that time.

From 2003 to 2015, the group was an active promoter and participant in the regional meetings of probability and mathematical statistics (ERPEM for the acronym in Spanish) organized jointly with research groups from Argentina, Brazil, and Chile. These events were relevant to strengthening the region's academic links and establishing sustained collaborations over time. The ERPEM had eleven editions, and Uruguay hosted these events several times.

The academic life of the group

Another relevant aspect where the group's activity is obtaining competitive financing sources for research projects. Especially in recent years, national funding has been obtained from organizations such as CSIC («Random geometry»; «Fluid boundary, diffusion approximation and large deviations in high-dimensional communication systems»), ANII, and MEC («Federated learning techniques for the analysis of sensitive data: application to the case of learning analytics»; «Genomic prediction with deep learning techniques», «Diffusions and operators: Interaction problems between local and non-local phenomena», etc.), other Udelar funds (Interdisciplinary Center for Data Science and Machine Learning (CICADA for its abbreviation in Spanish), etc., and international projects such as MathAmSud (José Rafael León is responsible for the project FANTASTIC: Statistical inFerence and sensitivity ANalysis for models described by sTochASTIC differential equations).

The daily academic exchange of the group is the Seminar of Probability and Statistics, where research works are presented by foreign researchers, members of the group, or members of other groups. Although the main focus of the seminar is probability and statistics, lectures from different disciplines are promoted, seeking to present problems that have a valuable mathematical component and can lead to interactions. In particular, links with engineering, computer science, physics, biology, and economics are encouraged. Since 2013, the group has been meeting on Friday mornings at the seminar. Before the virtualization, it was already transmitted by videoconference to various university sites in the country (mostly Salto and Rocha).

The Covid-19 pandemic

A seminar during the pandemic.

A critical point for the life of the seminar was the Covid-19 epidemic that reached the country in March 2020. At that time, the seminar organizers decided to dedicate the first semester and part of the second semester exclusively to modeling in epidemiology in general and Covid in particular. It constituted a space for discussion and proposals for understanding the dynamics of the epidemic, testing problems, and other related issues for the group.

In turn, several Probability and Statistics group members were part of GACH and GUIAD, which generated synergies for modeling, understanding (including active communication to the public), preparation of reports, and interaction with scientists from other disciplines.

In particular, a result of this period is the participation of Paola Bermolen and María Inés Fariello in the organization of the interdisciplinary Congress Covid-19 and some publications of the group. Currently, the group has a specific line of «Stochastic models in biology and epidemiology» where sub-lines associated with the Covid pandemic modeling are incorporated, derived from the period mentioned above.

Participation in academic programs and courses

The group also articulates the offer of undergraduate and graduate courses in probability and statistics. In particular, it is considered the possibility of offering courses and seminars of study for different levels of training, both basic and classical subjects, and more advanced topics linked to the group's research lines.

At the graduate level, the members of the group actively participate in the Master's Degree in Mathematical Engineering, the Master's Degree in Bioinformatics, the Master's Degree and Ph.D. in Mathematical Pedeciba, and more recently in the Master's Degree in Data Science and Machine Learning, offering courses, seminars and guiding students. It also participates in the evaluation and academic management of these graduate programs. In particular, in 2008, members of the group promoted the reformulation of the master's degree in Mathematical Engineering, which impacted the increase of students in the master's program and the diversity and quality of the courses offered. At the group level, this made it possible to broaden the profiles of students and young researchers in the area of probability and statistics. Several of them continued their doctoral studies in the area.

The cover image is a picture of a portrait of Pierre-Simon Laplace, founder of Probability and Statistics. It belogns to the article The origins of probability.