" Let us suppose that an individual, I , is provided with a certain set, C , of knowledge and that I ought to behave  dependently on the ocurrence or not of a given event, E ."

" ... the subjective notion of probability aims exactly to  measure this degree ... of belief... "

These are excerpts (translated from Portuguese) from the "Introduction to Probability Calculus" class notes used during the Fifties at ENCE (Escola Nacional de Ciencias Estatisticas - National School of Statistical  Siences) in Rio de Janeiro. The notes were written by Professor Rio Nogueira and constitute the earliest reference to subjective probability we have found in Brazilian writings. In fact, it is a nice surprise to find a Brazilian  relative I of de Finetti's character You !  [ENCE still exists and is na undergraduate school of Statistics maintained by IBGE , the Brazilian Census Institute. A few of the people mentioned below gratuated from ENCE].

Let us now move to the Sixties at Berkeley, where Caio Dantas, a probabilist from Sao Paulo, attended the seminars held by David Blackwell and Lester  Dubins. Dantas brought back a Bayesian seed (and also Blackwell's Basic Statistics book) to USP (Universidade de Sao Paulo) where Carlos Pereira wrote up a Bayesian MA dissertation. A few years later, Carlos went to Florida to get his PhD from Debabrata Basu. Upon his return to USP in the late Seventies, Bayesian activities in Brazilian  academia finally unfolded in a strong and regular fashion. The multiple - but always Bayesian - interests of Carlos Pereira influenced many researchers at Sao Paulo. Among his early PhD students we find the geneticist Andre Rogatko. Josemar Rodrigues was at USP faculty and wrote several papers jointly with Carlos Pereira on linear models and finite populations. Another faculty member, Heleno Bolfarine, returned from Berkeley in 1982 to start a brilliant career  on Bayesian theoretical statistics.

At that time in Rio Basilio Pereira, a student of Sir David Cox,  started to supervise some Bayesian students and hosted a first visit of Adrian Smith of three months in 1980. Basilio (Carlos' brother) proceeded and created the Bayesian atmosphere at UFRJ (Federal University of Rio de Janeiro) where Marlos Viana, Helio Migon and Dani Gamerman would later appear to make the department an excellence center on Bayesian research with sound contributions in econometrics, dynamical models, time series, epidemiology, survival analysis, stochastic simulation.

We are by now in the Eighties and our story becomes way less linear as the branches of the Brazilian Bayesian tree start to become many. At São  Paulo, Carlos Pereira, Josemar Rodrigues, Heleno Bolfarine and Jorge Achcar established a firm research activity and influenced many young people to follow Bayesian careers. Jose Galvao Leite wrote his PhD dissertation on Bayesian capture-recapture sampling under Carlos Pereira supervision. His MA students Telba Irony and Angela Mariotto went to get their doctoral degrees from Dick Barlow on Bayesian industrial engineering and Sir Cox, respectively. In Rio de Janeiro, Helio Migon and Dani Gamerman had returned from Warwick, having obtained their PhD degrees under the supervision of Jeff Harrison and Mike West, respectively.  Helio and Dani have been  supervising Bayesian dissertations since 1987 at COPPE/UFRJ (Graduate School of Engineering/UFRJ) and from now on at their home department, DME (Statistical Methods Department), which has just started to offer a regular PhD program in Bayesian Statistics.

During the Nineties, Bayesian activities in Brazil started to make good impact in other countries as foreign students returned to them. From USP Daniel Paulino returned to Portugal after getting a PhD from Carlos Pereira. Victor Salinas Torres and Pilar Iglesias, both from Chile and both Pereira's PhD students returned. Back in Chile, Pilar Iglesias has been provoking good Bayesian earthquakes since then. Luis Eduardo Montoya Delgado is back in Colombia after a superb PhD on DNA profiling for paternity investigation. Veronica Gonzalez-Lopez in Argentina is the most recent member of this impressive list of Carlos' PhD students. Paulino worked on identifiability, Torres on Bayesian non-parametrics and Dirichlet process, Pilar on predictivistic representations, and Lopez on Bayesian concepts of dependence. At the same department, Heleno  Bolfarine supervised students like Reynaldo Arellano Valle whose PhD dissertation won a first prize award at the Bernoulli Society Clapem contest. Valle is back in Chile and worked on external predivistic representations of elliptical families. Loretta Gasco at Peru and Patricia Gimenez at Mar del Plata were also  Bolfarine's doctoral students. Heleno Bolfarine and Pilar Iglesias were PhD advisers to Marcia Branco and Rosangela Loschi. All this people have very strong and active scientific collaboration. We have recent papers by Gonzalez-Lopez and Nelson Tanaka, Bolfarine and Valle and so on, not to mention Pilar Iglesias whose admirable drive puts almost everyone to work.

The brand new generation of Brazilian Bayesians includes Lurdes Inoue who after a PhD from Donald Berry at Duke is now at the MD Anderson Cancer Center at Houston and Hedibert Lopes who also graduated from Duke and is now at UFRJ faculty. Both got MA degrees in Brazil formerly, Lurdes from Sergio Wechsler and Hedibert from Helio Migon. A list of several almost-PhD Brazilian Bayesian students at USP, UFRJ, Duke, Sheffield .... could be  given but we prefer to hurry them up (not to mention that we intend to write the Second part of this story ten years from now).

Before getting too close to year 2000,  we should remember the series of bi-annual Bayesian Brazilian Seminars held since 1991. The first one was at Sao Carlos and chaired by Josemar  Rodrigues and Sergio Wechsler. In 1993, the Seminar was held jointly with the International Bayesian Hierarchical Meeting of Rio de Janeiro organized by  Dani Gamerman and Helio Migon and attended by Bayesians like Jose Bernardo, Adrian Smith and Phil Dawid (who would return for the third Brazilian Bayesian two years later). Before that , in 1992, we had in Rio a joint Brazil-US Meeting on Bayesian Econometrics chaired by Ruben Klein and attended by Arnold Zellner and J. Kadane among many others. [Omissions are unavoidable at this point and we apologize for this. Jim Berger, Susie Bayarri, Ed George, D.Poirier, S. Geisser, Alicia Carriquiry, Tony O'Hagan, Steven Fienberg, J. Press Luis Pericchi among again many others were also in Brazil a couple  of opportunities. The department at USP was visited  by Dev Basu, Dennis Lindley and Dick Barlow. Adrian Smith and Tony O'Hagan visited UFRJ more than once]. During the 1992 Meeting a vote was taken for the creation of ISBA.

Also during the Nineties a diffusion of Bayesian ideas and methods occurred  among researchers from other areas and statisticians and probabilists who would not consider themselves exclusively "Bayesians": we find outstanding contributions from Pablo Ferrari on Image Restoration, Antonio Galves on Linguistics, both at USP, Renato Assuncao at UFMG (Federal University at Minas Gerais) on Spatial Statistics and Disease Control, Pedro Morettin (USP) on Time Series.

We should also list the bibliographical contributions of Brazilian Bayesian authors: to mention books only, Heleno Bolfarine is co-author of S. Zacks'  book on Finite Populaton Estimation, Dani Gamerman wrote  " Monte Carlo Markov Chain: Stochastic Simulation for Bayesian Inference " and, jointly with Helio Migon, " Statistical Inference: an Integrated Approach " . Going back to the beginning, we find translations to Portuguese of Blackwell's Basic Statistics and  Raiffa's Decision Analysis already in the early Seventies. Carlos Pereira and Marlos Viana wrote a book in 1982 on Introductory Bayesian Statistics which was never translated from Portuguese.

Bayesian research activities are now very active in Brazilian universities with strong interaction with universities abroad. Last year the Brazilian  Bayesians decided to create a Brazilian Chapter of ISBA. The new Chapter made the decision to host the First " Latin American Bayesian Meeting " ( I COBAL) to be held very probably on January 2002 in Brazil.
 
 

The development of Bayesian statistics in Chile started only a few years ago. We all agree that Pilar Iglesias has been the spiritual leader of the group. After working with Carlos Pereira, she received the Doctoral degree from the U. of São Paulo (USP), Brazil. She later became a faculty member in the Department of Statistics of the P. U. Católica de Chile (PUC) in 1994.

 From the very day of her arrival at PUC, Pilar started making contact with faculty members at other universities. Consequently, the U. of La Serena, Chile hosted the First Bayesian Workshop, in January of 1996. It was a short
event, with a very reduced number of participants, but being the first entirely Bayesian meeting in Chile, it had a
special relevance. The workshop came as the result of a joint effort of Pilar, Victor Salinas from the U. de Santiago de Chile (USACH), another former student of C. Pereira in USP, and some local faculty members. Certainly, the whole project was strongly motivated by the Brazilian tradition.

Later, in May of 1996, the U. of Valparaíso (UV) hosted the First Workshop on Models with Errors in Variables and Bayesian Inference. Again, Pilar was at the heart of the organization, sharing responsibilities with Manuel Galea
of the UV, and Reinaldo Arellano (PUC), both former students of Heleno Bolfarine in USP. This was also the first time that the Journal of the Chilean Statistical Society (SOCHE) edited a special issue, completely devoted to the articles presented in this meeting.

The Second Workshop was hosted by the U. of Antofagasta (UA) in January of 1997. The local organizers were Héctor Varela, Guillermo Mondaca (former students of Vicente Quesada at U. Complutense de Madrid), and Juan Duarte
(former student of Domingo Morales, also at U. Complutense de Madrid), all of them faculty members of the UA.

The Third Workshop was held at the U. Austral de Chile in Valdívia (UAV) in January of 1998, where it was decided that the future versions would take place biannually. The local host was Eliana Scheihing from UAV (former student of Michel Mouchart in the U. of Louvain). A future issue of the SOCHE journal will concentrate on articles presented in Valdívia, this time including discussion. The Third Workshop had the largest international attendance so far, including Manuel Mendoza from ITAM in Mexico, Michel Mouchart and Heleno Bolfarine.

The Chilean chapter of ISBA was established in 1997. We currently have about 25 members from nearly all the universities in Chile, including some local graduate students and some current and former doctoral students in USP. The
reader is kindly invited to guess who has been the chair of our organization right from its birth.

The main topics of research conducted by Chilean Bayesians are: de Finetti-type Theorems (Pilar Iglesias); Bayesian modeling with errors in variables and with elliptical errors (Reinaldo Arellano, Pilar Iglesias, PUC;
Manuel Galea, UV); nonparametric Bayesian methods (Héctor Varela, Juan Duarte, Guillermo Mondaca, UA; Eliana Scheihing, UAV; Victor Salinas, USACH; Fernando Quintana, PUC); Bayesian modeling (Arturo Mora, María Elena
Valenzuela, U. de Concepcion; Ernesto San Martín, currently in U. Louvain). We also have to mention Alicia Carriquiry, from Iowa State U., Heleno Bolfarine, and Guido del Pino (PUC) who have repeatedly given us their support and encouragement in our research activities.

Bayesian statistics in Chile is at its early stages, but starting to grow and develop. Indeed, Pilar and Reinaldo have advised a number of Master theses at PUC, and some Ph. D. theses at USP. We expect to keep climbing the
ladder in the coming years.
 

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.
 
 

"Well, I have great respect for Bruno de Finetti and Harold Jeffreys, but you see Luis, here we are in the 10th floor of Evans Hall over viewing the Golden Gate. Bayesians have some work in the basement". Those were the words of J. Neyman to Luis Raúl Pericchi in 1978. Luis finished his Master and went to Imperial College in London to work on a
PhD under the supervision of A.C. Atkinson, working on a thesis on Information Theory together with Bayesian and Likelihood statistics for data transformations and model selection. Once he finished it he went back to Caracas, Venezuela, to work at Universidad Simón Bolívar were he started a Bayesian group.

The whole idea was motivated by the presence at USB, while Luis was a undergraduate student in the early seventies, of Ignacio Rodríguez Iturbe, who took a PhD in M.I.T. and went back to his home country to work at USB and the Instituto Venezolano de Investigaciones Científicas; he was very interested in the possible applications of Bayesian
statistics to hydrology, in particular, in how to enlarge limited information in some river basins, using regional information from other sites nearby. Ignacio motivated Luis Raúl and other students to work on Bayesian statistics and later made important contributions to its applications to hydrology. He nowadays holds a chair in Princeton, but he still is an influential figure in Venezuela.

The work in the basement started for Luis Raúl with a stats lab that was called TAE, "Taller de Estadística", within the Maths Department at USB. In the eighties TAE was a gathering place for statisticians and several students got interested in Bayesian statistics. I remember struggling with the 70Mb of disk space and the 8Mb of RAM memory of our
brand new Sun 3/110 workstation to squeeze in the code of Bayes 4 that Allan Skene brought us from Nottingham and the revolutionary New S that William Nazaret gave us from AT&T. Few years later, in '92, several faculty members of the areas of Numerical Analysis and Mathematical Programming, approached TAE, with the idea of forming a more comprehensive centre. A four years grant of 800,000 dollars from the Venezuelan Government, sponsored by the Interamerican Bank of Development, led to the creation of CESMa (Centro de Estadistica y Software Matematico), under the directorship of Marianela Lentini. The same year we organised one of Zellner's meetings on Bayesian statistics and econometrics, which was well attended by many statisticians from the Americas and left some people pondering the good properties of the añejo distribution for a while. The latest development of our group occurred in 1996 when the USB decided to form a new Department called "Department of Scientific Computing and Statistics", enhancing the importance of statistics within the university.

@ Our group

The hard core of Bayesians at USB is made of the following people:

   Víctor De Oliveira (vdo@cesma.usb.ve). Spent a year as a postdoc at the Institute of Statistical Sciences after taking a PhD at the University of Maryland College Park under the supervision of Benjamin Keden. He joined us in September '98 and works in spatial problems and geostatistics.

   María Eglée Pérez (eglee@cesma.usb.ve). Finished her PhD at Universidad Central de Venezuela in 1994 under the supervision of Luis Raúl Pericchi. She works in problems related to inference for the Exponential Family, Bayesian analysis of discrete data and biostatistics. She has a wonderful voice, well known among the public of the cabaret at
the last Valencia.

   José Miguel Pérez (jperez@cesma.usb.ve). He arrived to USB in September '98, from Purdue University where he finished a PhD under the supervision of Jim Berger. He works in methods related to automatic priors in particular mixture models with applications to the clustering and characterisation of variables.

   Luis Raúl Pericchi (pericchi@cesma.usb.ve). Took his PhD at Imperial College in 1981. He is the most senior member of our group and his work these days is very much focused on model comparison, with particular interest in non subjective priors, for which he and Jim Berger developed the Intrinsic Bayes Factor. His academic activities span a
wide range of topics including applications to medical statistics, engineering, econometrics and official statistics. He is known as a player of Brazilian guitar.

   Raquel Prado (raquel@cesma.usb.ve). She is back from North Carolina since September last year; there she took her PhD at the Institute of Statistics and Decision Sciences under the supervision of Mike West. She works in non stationary time series and applications of Bayesian methods to signal processing.

   Bruno Sansó (bruno@cesma.usb.ve). I finished my PhD at Universidad Central de Venezuela in 1992 as a student of Pericchi working on Bayesian robustness and spent some time at the University of Liverpool under the supervision of Phil Brown. I now work on spatio-temporal models with particular interest in environmental variables.

Other colleagues, with different degrees of Bayesianism share our statistical activities, they are:

  Lelys Guenni, PhD Griffith University, 1992. Spatio-temporal models for environmental variables, stochastic hydrology. In her last talk she promised that it was her last non-Bayesian one!

  Raúl Jiménez, PhD Universidad Central de Venezuela, 1992. Asymptotic behaviour of stochastic processes, theory of statistical information.

  Isabel Llatas, PhD Wisconsin-Madison, 1987. Experimental design, multivariate statistics, statistical quality assessment. She is currently the director of CESMa.

  José Luis Palacios, PhD Berkeley 1982. Random walks on graphs, discrete stochastic processes, combinatorics.

  Adolfo Quiroz, PhD MIT 1986. Nonparametric methods, goodness of fit for multivariate data.

  Leonardo Saab, Master Wisconsin Madison, 1985. Statistical applications of quality management, growth curves for Venezuelan children.

@ Working environment

USB has a very pleasant campus in the outskirts of Caracas, the capital of Venezuela. The weather is fairly mild thanks to the 1,000 plus meters above the sea level and the low density of the urban development around the campus. Tropical gardens, that are part of the university's pride, surround the buildings and create a very pleasant compare our
campus to a resort!

At CESMa we work mainly with Sun workstations, at last count they were around 16, the last arrival being a powerful 450 Enterprise with two processors. We have the tradition of naming them after characters of the Latin American literature and, as a result, we have a colourful network populated with thieves, whores, heroes, fantastic people
created by the imagination of García Márquez, Vargas Llosa and the like.

We have around 20 students following courses in three programmes: Diploma Master and PhD. All three programmes are quite new: they have been in place for less than two years, nevertheless they already seem to be a success.

We have definitely climbed some steps up from the basement during the last years and in spite of the uncertainties that we live these days in our country, I think that the future is bright for Bayesian statistics in Venezuela. This article is available in html with links and pictures at www.cesma.usb.ve/novedades/isbae.html .
 
 

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