Bruno de Finetti (13 June 1906 – 20 July 1985) was an Italian
probabilist statistician
A statistician is a person who works with Theory, theoretical or applied statistics. The profession exists in both the private sector, private and public sectors.
It is common to combine statistical knowledge with expertise in other subjects, a ...
and
actuary, noted for the "operational subjective" conception of
probability. The classic exposition of his distinctive theory is the 1937 , which discussed probability founded on the coherence of betting odds and the consequences of
exchangeability.
Life
De Finetti was born in
Innsbruck
Innsbruck (; ) is the capital of Tyrol (federal state), Tyrol and the List of cities and towns in Austria, fifth-largest city in Austria. On the Inn (river), River Inn, at its junction with the Wipptal, Wipp Valley, which provides access to the ...
, Austria, and studied mathematics at
Politecnico di Milano. He graduated in 1927, writing his thesis under the supervision of
Giulio Vivanti. After graduation, he worked as an actuary and a statistician at (
National Institute of Statistics) in Rome and, from 1931, the
Trieste
Trieste ( , ; ) is a city and seaport in northeastern Italy. It is the capital and largest city of the Regions of Italy#Autonomous regions with special statute, autonomous region of Friuli-Venezia Giulia, as well as of the Province of Trieste, ...
insurance company
Assicurazioni Generali. In 1936 he won a competition for Chair of Financial Mathematics and Statistics, but was not nominated due to a fascist law barring access to unmarried candidates;
he was appointed as ordinary professor at the
University of Trieste only in 1950.
He published extensively (17 papers in 1930 alone, according to Lindley) and acquired an international reputation in the small world of probability mathematicians. He taught
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...
in Padua and then won a chair in Financial Mathematics at
Trieste University (1939). In 1954 he moved to the
Sapienza University of Rome, first to another chair in Financial Mathematics and then, from 1961 to 1976, one in the Calculus of Probabilities. De Finetti developed his ideas on subjective probability in the 1920s independently of
Frank P. Ramsey. Still, according to the preface of his "Theory of Probability", he drew on ideas of
Harold Jeffreys,
I. J. Good and
B. O. Koopman. He also reasoned about the connection of economics and probability, and thought that guiding principles to be
Paretian optimum further inspired by "fairness" criteria. De Finetti held different social and political beliefs through his life: following
fascism
Fascism ( ) is a far-right, authoritarian, and ultranationalist political ideology and movement. It is characterized by a dictatorial leader, centralized autocracy, militarism, forcible suppression of opposition, belief in a natural social hie ...
during his youth, then moving to
Christian socialism and finally adhering to the
Radical Party.
De Finetti only became known in the Anglo-American statistical world in the 1950s when
L. J. Savage, who had independently adopted
subjectivism, drew him into it; another great champion was
Dennis Lindley. De Finetti died in Rome in 1985.
Work and impact
De Finetti emphasized a
predictive inference approach to statistics; he proposed a
thought experiment along the following lines (described in greater detail at
coherence): ''You'' must set the price of a promise to pay $1 if there was life on Mars 1 billion years ago, and $0 if there was not, and tomorrow the answer will be revealed. You know that ''your opponent'' will be able to choose either to buy such a promise from you at the price you have set, or require you to buy such a promise from your opponent, still at the same price. In other words: you set the odds, but your opponent decides which side of the bet will be yours. The price you set is the "operational subjective probability" that you assign to the proposition on which you are betting. This price has to obey the probability axioms if you are not to face certain loss, as you would if you set a price above $1 (or a negative price). By considering bets on more than one event, de Finetti could justify additivity. Prices, or equivalently odds, that do not expose you to certain loss through a ''
Dutch book'' are called ''coherent''.
De Finetti is also noted for
de Finetti's theorem on exchangeable sequences of
random variables. De Finetti was not the first to study exchangeability, but he brought the subject to greater visibility. He started publishing on exchangeability in the late 1920s, but his 1937 article "La Prévision" (see bibliography) is his most famous treatment.
In 1929, de Finetti introduced the concept of
infinitely divisible probability distributions.
He also introduced
de Finetti diagrams for graphing
genotype frequencies.
The 1974 English translation of his book is credited with reviving interest in predictive inference in the Anglophone world and bringing the idea of exchangeability to its attention.
Predictive Inference: An Introduction
', Seymour Geisser, CRC Press, 1993, .
In 1961 he was elected as a
Fellow of the American Statistical Association.
The de Finetti Award, presented annually by the
European Association for Decision Making, is named after him. The Department of Mathematics, Statistics and Economics of the
University of Trieste is named after him too.
In the 21st century
quantum extensions of de Finetti's representation theorem have been found to be useful in
quantum information, in topics like
quantum key distribution and
entanglement detection.
Bibliography
See Works on
Bruno de Finetti website
de Finetti in English
(The following are translations of works originally published in Italian or French.)
*"Probabilism: A Critical Essay on the Theory of Probability and on the Value of Science," (translation of 1931 article) in ''Erkenntnis,'' volume 31, issue 2–3, September 1989, pp. 169–223. The entire double issue is devoted to de Finetti's philosophy of probability.
* 1937, "La Prévision: ses lois logiques, ses sources subjectives," Annales de l'Institut Henri Poincaré,
: - "Foresight: its Logical Laws, Its Subjective Sources," (translation of th
1937 articlein French) in H. E. Kyburg and H. E. Smokler (eds), ''Studies in Subjective Probability,'' New York: Wiley, 1964.
*''Theory of Probability'', (translation by A Machi and
AFM Smith of 1970 book) 2 volumes, New York: Wiley, 1974–1975.
Discussions
*
D. V. Lindley, "Bruno de Finetti, 1906-1985 (Obituary)" ''
Journal of the Royal Statistical Society, Series A'', 149, p. 252 (1986).
The following books have a chapter on de Finetti and references to further literature.
*Jan von Plato, ''Creating Modern Probability: Its Mathematics, Physics, and Philosophy in Historical Perspective'', Cambridge: Cambridge University Press, 1994
*Donald Gillies, ''Philosophical Theories of Probability'', London: Routledge, 2000.
See also
*
Exchangeability
*
Quasiconvex function
References
External links
*
Probabilità e induzione', Bologna, 1993.
Bruno de Finetti websiteGenerate finetti diagrams online*Bruno de Finetti's Paper
Bruno de Finetti Papers, 1924–2000, ASP.1992.01, Archives of Scientific Philosophy, Special Collections Department, University of Pittsburgh)
De Finettion th
page.
Interpretations of Probabilityfrom the Stanford Encyclopedia of Philosophy. De Finetti's views are discussed in Section 3.5 of this article.
''Bruno de Finetti e la geometria del benessere''by Rosaria Adriani
{{DEFAULTSORT:Finetti, Bruno De
1906 births
1985 deaths
Italian actuaries
20th-century Italian mathematicians
Italian statisticians
Probability theorists
Philosophers of probability
Bayesian statisticians
Bayesian econometricians
20th-century Italian economists
Fellows of the Econometric Society
Fellows of the American Statistical Association
Scientists from Innsbruck
Austrian emigrants to Italy
Academic staff of the University of Trieste
Academic staff of the Sapienza University of Rome
Mathematical statisticians