Bruno de Finetti (13 June 1906 – 20 July 1985) was an Italian
probabilist statistician
A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors.
It is common to combine statistical knowledge with expertise in other subjects, and statisticians may wor ...
and
actuary
An actuary is a business professional who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science. These risks can affect both sides of the balance sheet and require asset man ...
, noted for the "operational subjective" conception of
probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...
. The classic exposition of his distinctive theory is the 1937 "La prévision: ses lois logiques, ses sources subjectives," which discussed probability founded on the coherence of betting odds and the consequences of
exchangeability In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence ''X''1, ''X''2, ''X''3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change whe ...
.
Life
De Finetti was born in
Innsbruck
Innsbruck (; bar, Innschbruck, label=Bavarian language, Austro-Bavarian ) is the capital of Tyrol (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 ...
, Austria, and studied mathematics at
Politecnico di Milano
The Polytechnic University of Milan () is the largest technical university in Italy, with about 42,000 students.
The university offers undergraduate, graduate and higher education courses in engineering, architecture and design.
Founded in 186 ...
. He graduated in 1927 writing his thesis under the supervision of
Giulio Vivanti. After graduation, he worked as an actuary and a statistician at ''Istituto Nazionale di Statistica'' (
National Institute of Statistics) in Rome and, from 1931, the
Trieste
Trieste ( , ; sl, Trst ; german: Triest ) is a city and seaport in northeastern Italy. It is the capital city, and largest city, of the autonomous region of Friuli Venezia Giulia, one of two autonomous regions which are not subdivided into provi ...
insurance company
Assicurazioni Generali
Assicurazioni Generali S.p.A. ( , ; meaning 'general insurances') or simply Generali Group is an Italian insurance company based in Trieste. As of 2019, it is the largest of its kind in Italy and among the top ten largest insurance companies in ...
. 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
The University of Trieste ( it, Università degli Studi di Trieste, or UniTS) is a public research university in Trieste in the Friuli-Venezia Giulia region in northeast Italy. The university consists of 10 departments, boasts a wide and almos ...
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 (m ...
in Padua and then won a chair in Financial Mathematics at
Trieste University (1939). In 1954 he moved to the
Sapienza University of Rome
The Sapienza University of Rome ( it, Sapienza – Università di Roma), also called simply Sapienza or the University of Rome, and formally the Università degli Studi di Roma "La Sapienza", is a Public university, public research university l ...
, 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
Frank Plumpton Ramsey (; 22 February 1903 – 19 January 1930) was a British philosopher, mathematician, and economist who made major contributions to all three fields before his death at the age of 26. He was a close friend of Ludwig Wittgenste ...
. Still, according to the preface of his Theory of Probability, he drew on ideas of
Harold Jeffreys
Sir Harold Jeffreys, FRS (22 April 1891 – 18 March 1989) was a British mathematician, statistician, geophysicist, and astronomer. His book, ''Theory of Probability'', which was first published in 1939, played an important role in the revival ...
,
I. J. Good
Irving John Good (9 December 1916 – 5 April 2009)The Times of 16-apr-09, http://www.timesonline.co.uk/tol/comment/obituaries/article6100314.ece
was a British mathematician who worked as a cryptologist at Bletchley Park with Alan Turing. Afte ...
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, ultra-nationalist political ideology and movement,: "extreme militaristic nationalism, contempt for electoral democracy and political and cultural liberalism, a belief in natural social hierarchy an ...
during his youth, then moving to
Christian socialism
Christian socialism is a religious and political philosophy that blends Christianity and socialism, endorsing left-wing politics and socialist economics on the basis of the Bible and the teachings of Jesus. Many Christian socialists believe capi ...
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
Subjectivism is the doctrine that "our own mental activity is the only unquestionable fact of our experience", instead of shared or communal, and that there is no external or objective truth.
The success of this position is historically attribute ...
, drew him into it; another great champion was
Dennis Lindley
Dennis Victor Lindley (25 July 1923 – 14 December 2013) was an English statistician, decision theorist and leading advocate of Bayesian statistics.
Biography
Lindley grew up in the south-west London suburb of Surbiton. He was an only child an ...
. De Finetti died in Rome in 1985.
Work and Impact
De Finetti emphasized a
predictive inference
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers propertie ...
approach to statistics;
he proposed a
thought experiment
A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences.
History
The ancient Greek ''deiknymi'' (), or thought experiment, "was the most anci ...
along the following lines (described in greater detail at
coherence (philosophical gambling strategy)
In a thought experiment proposed by the Italian probabilist Bruno de Finetti in order to justify Bayesian probability, an array of wagers is coherent precisely if it does not expose the wagerer to certain loss regardless of the outcomes of events ...
): ''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
In gambling, a Dutch book or lock is a set of odds and bets, established by the bookmaker, that ensures that the bookmaker will profit—at the expense of the gamblers—regardless of the outcome of the event (a horse race, for example) on which ...
'' are called ''coherent''.
De Finetti is also noted for
de Finetti's theorem
In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some latent variable. An epistemic probability distribution could then be assigned to this variable. It is named in hono ...
on exchangeable sequences of
random variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
s. 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 the 1937 article is his most famous treatment.
In 1929, de Finetti introduced the concept of
infinitely divisible probability distributions.
He also introduced
de Finetti diagram
A de Finetti diagram is a ternary plot used in population genetics. It is named after the Italian statistician Bruno de Finetti (1906–1985) and is used to graph the genotype frequencies of populations, where there are two alleles and the popul ...
s for graphing
genotype
The genotype of an organism is its complete set of genetic material. Genotype can also be used to refer to the alleles or variants an individual carries in a particular gene or genetic location. The number of alleles an individual can have in a ...
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 Seymour Geisser (October 5, 1929 – March 11, 2004) was an American statistician noted for emphasizing predictive inference. In his book ''Predictive Inference: An Introduction'', he held that conventional statistical inference about unobservable ...
, CRC Press
The CRC Press, LLC is an American publishing group that specializes in producing technical books. Many of their books relate to engineering, science and mathematics. Their scope also includes books on business, forensics and information tec ...
, 1993
In 1961 he was elected as a
Fellow of the American Statistical Association
Like many other academic professional societies, the American Statistical Association (ASA) uses the title of Fellow of the American Statistical Association as its highest honorary grade of membership. The number of new fellows per year is limited ...
.
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
The University of Trieste ( it, Università degli Studi di Trieste, or UniTS) is a public research university in Trieste in the Friuli-Venezia Giulia region in northeast Italy. The university consists of 10 departments, boasts a wide and almos ...
is named after him too.
In the 21'st century
quantum extensions of de Finetti's representation theorem have been found to be useful in
quantum information
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...
, in topics like
quantum key distribution
Quantum key distribution (QKD) is a secure communication method which implements a cryptographic protocol involving components of quantum mechanics. It enables two parties to produce a shared random secret key known only to them, which can then be ...
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
Sir Adrian Frederick Melhuish Smith, PRS (born 9 September 1946) is a British statistician who is chief executive of the Alan Turing Institute and president of the Royal Society.
Early life and education
Smith was born on 9 September 1946 in ...
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
The ''Journal of the Royal Statistical Society'' is a peer-reviewed scientific journal of statistics. It comprises three series and is published by Wiley for the Royal Statistical Society.
History
The Statistical Society of London was found ...
'', 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
*
Coherence (philosophical gambling strategy)
In a thought experiment proposed by the Italian probabilist Bruno de Finetti in order to justify Bayesian probability, an array of wagers is coherent precisely if it does not expose the wagerer to certain loss regardless of the outcomes of events ...
*
De Finetti diagram
A de Finetti diagram is a ternary plot used in population genetics. It is named after the Italian statistician Bruno de Finetti (1906–1985) and is used to graph the genotype frequencies of populations, where there are two alleles and the popul ...
*
De Finetti's theorem
In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some latent variable. An epistemic probability distribution could then be assigned to this variable. It is named in hono ...
*
Exchangeability In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence ''X''1, ''X''2, ''X''3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change whe ...
*
Infinitely divisible probability distributions
Infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also a branch of mathematics). One may speak of infinite divisibility, or the lack thereof, of matter, ...
*
Predictive inference
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers propertie ...
*
Quasiconvex function
In mathematics, a quasiconvex function is a real-valued function defined on an interval or on a convex subset of a real vector space such that the inverse image of any set of the form (-\infty,a) is a convex set. For a function of a sing ...
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
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
University of Trieste faculty
Sapienza University of Rome faculty