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A CONVERSATION with EUGENIO REGAZZINI 3 Prize in Economics in 1985

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A CONVERSATION with EUGENIO REGAZZINI 3 Prize in Economics in 1985 Statistical Science 2011, Vol. 26, No. 4, 647–672 DOI: 10.1214/11-STS362 c Institute of Mathematical Statistics, 2011 A Conversation with Eugenio Regazzini Antonio Lijoi1 and Igor Pr¨unster1 Abstract. Eugenio Regazzini was born on August 12, 1946 in Cremona (Italy), and took his degree in 1969 at the University “L. Bocconi” of Milano. He has held positions at the universities of Torino, Bologna and Milano, and at the University “L. Bocconi” as assistant professor and lec- turer from 1974 to 1980, and then professor since 1980. He is currently professor in probability and mathematical statistics at the University of Pavia. In the periods 1989–2001 and 2006–2009 he was head of the Insti- tute for Applications of Mathematics and Computer Science of the Italian National Research Council (C.N.R.) in Milano and head of the Depart- ment of Mathematics at the University of Pavia, respectively. For twelve years between 1989 and 2006, he served as a member of the Scientific Board of the Italian Mathematical Union (U.M.I.). In 2007, he was elected Fellow of the IMS and, in 2001, Fellow of the “Istituto Lombardo—Accademia di Scienze e Lettere.” His research activity in probability and statistics has covered a wide spectrum of topics, including finitely additive probabili- ties, foundations of the Bayesian paradigm, exchangeability and partial exchangeability, distribution of functionals of random probability mea- sures, stochastic integration, history of probability and statistics. Overall, he has been one of the most authoritative developers of de Finetti’s legacy. In the last five years, he has extended his scientific interests to probabilistic methods in mathematical physics; in particular, he has studied the asymp- totic behavior of the solutions of equations, which are of interest for the kinetic theory of gases. The present interview was taken in occasion of his 65th birthday. Key words and phrases: Bayesian inference, Dirichlet process, exchange- ability, de Finetti, finitely additive probabilities, History of Statistics and Probability in Italy, subjective probability. arXiv:1205.4807v1 [stat.OT] 22 May 2012 1. PROBABILITY AND STATISTICS AT BOCCONI UNIVERSITY Antonio Lijoi is Associate Professor of Statistics at the Department of Economics and Quantitative Methods, Antonio: You received your degree in economics University of Pavia, via San Felice 5, 27100 Pavia, from “L. Bocconi” University in Milano. Why did Italy e-mail: [email protected]. Igor Pr¨unster is Associate you decide to study economics? Professor of Statistics at the Department of Applied Eugenio: I enrolled in an economics degree essen- Mathematics and Statistics “Diego De Castro,” tially because it was the only choice I had. Hav- University of Torino, c.so Unione Sovietica 218/bis, ing attended a Technical High School for Accoun- 10134 Torino, Italy e-mail: [email protected]. tants, at the time the law did not allow students 1 Also affiliated to Collegio Carlo Alberto, Moncalieri, Italy. from this kind of secondary school to study mathe- This is an electronic reprint of the original article matics at university, which would have been my fa- published by the Institute of Mathematical Statistics in vorite option. You needed to attend college prepara- Statistical Science, 2011, Vol. 26, No. 4, 647–672. This tory schools to enroll in subjects like mathematics. reprint differs from the original in pagination and My family could not afford my university studies typographic detail. and I was expected to get a job right after com- 1 2 A. LIJOI AND I. PRUNSTER¨ pleting high school. The choice I made at the age 1970s when the first full professors in probability, of 14 was coherent with this scenario. By the time apart from de Finetti, were recruited after national I got my diploma from high school, the situation competitions. Turning back to Vailati, it is worth had improved a little bit and I could afford going recalling that, among some courses for high school to university. This was also due to a financial aid teachers organized by the Italian Ministry of Educa- program, adopted by the farseeing Italian center— tion, he also took a course in probability, which was left governments of the time, for students belonging delivered by de Finetti. As a consequence, at the to economically disadvantaged families. The money age of 16 I was introduced to the realm of subjec- from this program (it was around 200 euros, per tivism and learned the first elements of probability year, in 1965) and the earnings deriving from private and its applications. These first years of exposure to lessons I used to teach to other students allowed me de Finetti’s approach have stimulated an intellectual to obtain a degree at Bocconi University. and scientific interest that has certainly influenced Igor: Why did you choose Bocconi University and my later research. not another university? A: How was the environment at Bocconi Univer- E: In the 1960s Bocconi was considered a presti- sity in the years you have been there? gious university: a degree from it represented the key E: Bocconi had very few professors among its own for obtaining a good and rewarding job on the mar- faculty and heavily relied upon adjunct faculty hold- ket. These elements exerted an influence on me and ing positions in other universities. These few pro- my family. However, there was also a practical rea- fessors were all influential personalities of the time, son: Milano is just one hour by train from my home- playing significant roles in the Italian social, polit- town, Cremona, and I could go back home every ical and economic life of the 1960s. For instance, weekend. Yet another reason is the influence of my Giovanni Demaria was a Paretian economist who friend Lorenzo Peccati, a mathematical economist acted as economic consultant for the constituent as- from Cremona, who was a student at Bocconi while sembly that created the Constitution that lies at I was still at high school. He was well aware of my the foundation of the modern Italian Republic after bent for mathematics and suggested a few advanced World War II. There was also a special feeling be- textbooks where I started reading the mathemati- tween Bocconi and Milano, a city that had been able cal tools used in economic modeling. In particular, to overcome the disasters of World War II and was I was excited at reading the Italian translation of the experiencing dramatic economic growth led by the monograph Allen (1956) on mathematical analysis manufacturing sector. Bocconi looked to me, and for economists and this convinced me that Bocconi many others, as a vital part of Milano and con- would still have allowed me to study Maths. tributed to consolidate this process. Then, during I: This is a funny coincidence since I was con- the last couple of years, the student protests of 1968 vinced by Lorenzo Peccati’s son, Giovanni, by now started. Despite being a private university, Bocconi a well-known probabilist, to enroll at Bocconi and experienced serious clashes and some of its students for precisely the same reasons. Where did your pas- played an active role in the movement. sion for mathematics come from? I: Did you like studying economics? E: I was very lucky at high school because I had E: I was very fond of economics. The professors a brilliant maths teacher, Sidomo Vailati. He had I was interacting with were quite enthusiastic about a variety of scientific and cultural interests and also my inclination toward developing mathematical tools did consulting for a few private companies, thanks useful for economic modeling. There is an episode to his unusual, at least in that period, knowledge that occurred during my third year that I like to of statistics, probability and operations research. He recall. I was attending a course in Political economy certainly was a self-taught man in the area of Stochas- which included a series of seminars and one of them tics. At that time, probability and statistics, unlike concerned the relationship between the Italian Cen- analysis, geometry and algebra, were not perceived tral Bank and the Department of Treasury, which as relevant topics within mathematics degrees: they at that time was the subject of a lively debate. For were only present in a few optional courses. To my an economic interpretation of the relationship be- knowledge, the only exception was the University tween the two institutions, we were suggested to re- of Roma due to the presence of Bruno de Finetti. fer to an article by Giorgio La Malfa and Franco In fact, this unfortunate situation lasted until the Modigliani; the latter was later awarded the Nobel A CONVERSATION WITH EUGENIO REGAZZINI 3 prize in economics in 1985. The main contribution of A: And how did it work out? What were your first the paper was the proposal of a static model. Playing impressions on the Bayesian approach? a bit around with that model, I was able to derive E: While working on the thesis, I developed some a dynamic version of it, which seemed in line with skepticism about the automatic implementation of the real situation in Italy. This was appreciated by Bayes’ theorem, which was a legacy from Laplace the other students and the teaching assistants. Also and his followers. However, my viewpoint was lim- in connection with the course on Public Finance, ited. In fact, writing the thesis was not an easy job, I devised a model describing the evolution of cer- especially because I could not rely on many sys- tain taxing decisions. Overall, I think I had quite tematic and exhaustive treatments. There were, of a good economic intuition. course, de Finetti’s papers, but, given the unortho- A: What did lead you to study probability and dox way they were written, I was not able to un- statistics? derstand the connection between his theory and the E: I was both impressed and fascinated by the first Anglo-American neo-Bayesian approach typically year course in mathematics that was taught by Gio- adopted in papers appearing in statistics journals vanni Ricci.
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