(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 Cálculo (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-Peña (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 Peña 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.