Bayesianismo - História: México

Bayesians in Mexico
by Manuel Mendoza


The history of Bayesian Statistics as well as that of Statistics as an independent scientific discipline in Mexico is rather brief. I shall refer to the beginnings just by paraphrasing Mendoza and Méndez (1991).

The first PhD in Statistics obtained by a Mexican citizen was awarded to Basilio Rojas in 1959 at the Iowa State University. The first formal master program on Statistics was created at the Centro de Estadística y Calculo (CEC) of the Colegio de Posgraduados de Chapingo in 1964 and one year later there were only three Mexicans with a doctoral degree in Statistics. In 1969, a master program in Statistics and Computing was created at the CEC.

During the following years some other master programs were created, most of them with a specific orientation to some field of application. Thus, in 1966 a program in Statistics was created at the Colegio de México (an institution oriented to economical and sociological studies). In 1973, a Master of Science program in Mathematical Statistics was created at the Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS) of the National University.

As for the Bayesian approach to Statistics, the subject appeared as part of the courses taught by Prof. Basilio Rojas at the CEC since 1964. However, it was only in 1973, at the IIMAS, that the first graduate course on Bayesian Statistics was included in a master program (as an elective course).

According to the available information, I believe that the first Bayesian doctoral dissertation by a Mexican was that of Enrique de Alba who in 1974 got his PhD in Statistics from the University of Wisconsin at Madison. In his thesis he proposed a procedure to deal with outliers using an Empirical Bayes approach.

The interest for the Bayesianism in México has been stimulated by some important events. Some colleagues remember that in 1974, a seminar was organised by the Colegio de Posgraduados to which several prominent statisticians were invited. Among these, Prof. G.E.P. Box was very enthusiastic about the Bayesian methods and the audience was really impressed by his talk. Another definitive influence can be attributed to the long-term relationship that Prof. José Miguel Bernardo, from Valencia University, established with some Mexican statisticians.

The first time that José visited México was in 1979. He offered a one-month intensive course on the foundations of Bayesian Statistics at the Facultad de Ciencias of the National University. José is well known to be one of the most radical Bayesians all over the world and one month of this Bernardian influence could not be ignored. As one of the many results of that visit, a second Bayesian doctoral thesis was produced. In this case, it was a thesis submitted by Gustavo Valencia to obtain a PhD in Mathematics from the National University. To this purpose, he spent one year in Valencia in 1983 working under the supervision of José on the problem of regression analysis with incomplete observations.

In 1984, Bernardo repeated the dose. Another one-month intensive course was organised, again at the Facultad de Ciencias, now on Bayesian methods and some specific applications. As a particular consequence of this second visit, Manuel Mendoza who was interested in the analysis of bioassays, asked José to be his PhD supervisor at the National University. Manuel spent two years (1985-1987) in Valencia where he completed an investigation on the inference for the ratio of linear combinations of the coefficients of a regression model. This thesis was presented in 1988 and José was a member of the examination committee. This was his third visit to the National University although on that occasion he was hosted by the IIMAS.

Since then, Bernardo has continued his visits to México; he came back in 1992 invited by Manuel Mendoza on behalf of the Instituto Tecnológico Autónomo de México (ITAM). He visited the IIMAS again in 1997 and, in addition, he has been invited as speaker to a number of events in México. The most important are the II Congreso Iberoamericano de Estadística in 1995, the XII Foro Nacional de Estadística in 1997, the Taller Mexicano de Estadística Bayesiana in 1998 and the III International Workshop on Objective Bayesian Methodology in 2000. The relation between José and us has been fruitful in many ways. Some of us maintain active research projects with him and right now another Mexican, Miguel Angel Juárez from ITAM, is currently Bernardo´s graduate student at Valencia.

Just to summarise, up to 1988 three Mexican statisticians had obtained a doctoral degree with a thesis on Bayesian Statistics. Fortunately, the situation has been evolving very rapidly. In the 90's, an important number of students decided to work for their Master degree or their PhD in Bayesian Statistics at some prominent universities. E. de Alba and M. Mendoza at ITAM encouraged many of these students and some others were benefited from the influence of R. Rueda at IIMAS.

The universities where those colleagues studied are Imperial College of Science, Technology and Medicine, Warwick University, Nottingham University, Sheffield University, Essex University and Oxford University all of them in the United Kingdom. In the U.S. the favourite university has been, without any doubt, Duke followed by Chicago.

At least ten Mexicans have recently obtained a PhD in Bayesian Statistics (or some other related fields). They are: Andrés Christen (1994), Eduardo Gutiérrez-Pena (1995), Raúl Rueda (1995), Rubén Haro (1997), Gabriel Huerta (1998), Juan José Fernández (1998), Omar Aguilar (1998), Rafael Perera (1999), Viridiana Lourdes de León (2000) and Luis Enrique Nieto (2001).

In addition, around ten students from ITAM have obtained a master degree in Statistics at Warwick University and nowadays, we have some students working for their PhD at Sheffield, Warwick, Chicago and Valencia universities.

The community of Mexican Bayesians has been affiliated, for the most part, with the universities but some of them work at the government and the corporate world. The larger research groups are now at the Statistics Department of ITAM and the Probability and Statistics Department at IIMAS and some other colleagues are very active at the Instituto de Matemáticas (IMATE) of the National University and the Centro de Investigación en Matemáticas (CIMAT).

The range of topics that they work on includes: Model selection, reference analysis, dynamic linear models, general inference for exponential families, sample size determination, time series, hypotheses testing, nonparametric analysis, linear models, classification procedures, survival analysis, branching processes as well as applications to finance, image restoration, actuarial sciences, archaeology, bioassays and election forecasting.

Another two facts might be of some interest. Firstly, the number and the nature of the events that Mexican Bayesians have organised. In 1986 a NSF-NBER Seminar on Bayesian Inference in Econometrics took place at ITAM with the strong support of Prof. Arnold Zellner. Later, in 1995, the World Meeting of ISBA was held in Oaxaca immediately after the II Congreso Iberoamericano de Estadística. Two workshops, under the name of Taller Mexicano de Estadística, were organised in 1998 and 1999. The invited speakers for these workshops were Susie Bayarri, James Berger, Dani Gamerman, José Bernardo and Andrew Gelman. Although the annual national statistical meeting has never been a Bayesian conference, several times they have included Bayesian invited speakers as, for example, José Bernardo, James Berger, Daniel Pena and Javier Girón among others. More recently, in 2000 the III International Workshop on Objective Bayesian Methodology was held in Ixtapa.

The other relevant aspect is the fact that the rather small Mexican Bayesians group has published papers in some of the most important statistical journals. Just to mention a few, papers have appeared in the following journals: Royal Statistical Society, series B, C and D, Journal of Applied Statistics, Biometrics, Journal of the American Statistical Association, Journal of Business and Economic Statistics, Biometrical Journal, TEST, Journal of Statistical Planning and Inference, Journal of Statistics and the North American Actuarial Journal.

Reference: Mendoza, M. and Mendez, I. (1991). Graduate Statistical Training in México. ESTADISTICA, 43, 140, 101-113.

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