Bruno de Finetti (Innsbruck, June 13, 1906 - Rome, July 20, 1985) was an Italian probabilist and statistician, noted for the "operational subjective" conception of probability. The classic exposition of his distinctive theory is the 1937 "La prévision: ses lois logiques, ses sources subjectives," Annales de l'Institut Henri Poincaré, 7, 1-68, which discussed probability founded on the coherence of betting odds and the consequences of exchangeability. Innsbruck City Center Innsbruck and Nordkette from south // Geography Innsbruck is a city in western Austria, and the capital of the Tyrol province. ... June 13 is the 164th day of the year in the Gregorian calendar (165th in leap years), with 201 days remaining. ... 1906 was a common year starting on Monday (see link for calendar). ... City motto: Senatus Populusque Romanus – SPQR (The Senate and the People of Rome) Founded 21 April 753 BC mythical, 1st millennium BC Region Latium Mayor Walter Veltroni (Left-Wing Democrats) Area  - City Proper  1290 km² Population  - City (2004)  - Metropolitan  - Density (city proper) 2,546,807 almost 4,000,000 1... July 20 is the 201st day (202nd in leap years) of the year in the Gregorian Calendar, with 164 days remaining. ... This article is about the year. ... A probabilist is either a mathematician specializing in probability theory, or one who espouses probabilism in theology or philosophy. ... For Wikipedia statistics, see m:Statistics Statistics is the science and practice of developing human knowledge through the use of empirical data expressed in quantitative form. ... The word probability derives from the Latin probare (to prove, or to test). ...

De Finetti proposed a thought experiment along the following lines (described in great detail at coherence (philosophical gambling strategy)): 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. In philosophy, physics, and other fields, a thought experiment (from the German Gedankenexperiment) is an attempt to solve a problem using the power of human imagination. ... 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 if his opponent is prudent. ... In probability theory and statistics the odds in favor of an event or a proposition are the quantity p / (1 − p), where p is the probability of the event or proposition. ... In gambling a Dutch book or lock is a set of odds and bets which guarantees a profit, no matter what the outcome of the gamble. ...

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 put the subject on the map. He started publishing on exchangeability in the late 1920s but the 1937 article is his most famous treatment. In probability theory, de Finettis theorem explains why exchangeable observations are conditionally independent given some (usually) unobservable quantity to which an epistemic probability distribution would then be assigned. ... In probability theory, de Finettis theorem explains why exchangeable observations are conditionally independent given some (usually) unobservable quantity to which an epistemic probability distribution would then be assigned. ... A random variable can be thought of as the numeric result of operating a non-deterministic mechanism or performing a non-deterministic experiment to generate a random result. ...

In 1929, de Finetti introduced the concept of infinitely divisible probability distributions. The concept of infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also a branch of mathematics). ...

De Finetti studied mathematics at Milan University. After graduation, he did not pursue an academic career but worked as an actuary and a statistician. He published extensively (17 papers in 1930 alone, according to Lindley) and acquired an international reputation in the small world of probability mathematicians. He won a chair in Financial Mathematics at Trieste University (1939). In 1954 he moved to the 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. He 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. Frank Plumpton Ramsey (February 22, 1903 – January 19, 1930) was a British mathematician, philosopher and economist. ... Leonard Jimmie Savage (20 November 1917 - 1 November 1971) was a US mathematician and statistician. ... Bayesian inference is a statistical inference in which probabilities are interpreted not as frequencies or proportions or the like, but rather as degrees of belief. ...

Bibliography

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, September 1989. The entire double issue is devoted to de Finetti's philosophy of probability.
• "Foresight: its Logical Laws, Its Subjective Sources," (translation of the 1937 article in French) in H. E. Kyburg and H. E. Smokler (eds), Studies in Subjective Probability, New York: Wiley, 1964.
• Theory of Probability, (translation of 1970 book) 2 volumes, New York: Wiley, 1974-5.

1989 (MCMLXXXIX) is a common year starting on Sunday of the Gregorian calendar. ...

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 Theory, Cambridge: Cambridge University Press, 1994
• Donald Gillies, Philosophical Theories of Probability, London: Routledge, 2000.

External links

• Interpretations of Probability from the Stanford Encyclopedia of Philosophy. De Finetti's views are discussed in Section 3.5 of this article.

• MacTutor: Bruno de Finetti

There is another photo at

• de Finetti on the Portraits of Statisticians page.