Bruno de Finetti
Encyclopedia
Bruno de Finetti was an Italian
probabilist, statistician
and actuary
, 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," which discussed probability founded on the coherence of betting odds and the consequences of exchangeability.
, 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
insurance company Assicurazioni Generali
.
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 in Padua and then 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
. 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 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
.
approach to statistics;
he proposed a thought experiment
along the following lines (described in greater 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.
De Finetti is also noted for de Finetti's theorem
on exchangeable
sequences of random variable
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
s 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.
The de Finetti Award, presented annually by the European Association for Decision Making, is named after him.
The following books have a chapter on de Finetti and references to further literature.
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
probabilist, statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
and actuary
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....
, noted for the "operational subjective" conception of probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
. 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.
Life
De Finetti was born in InnsbruckInnsbruck
- Main sights :- Buildings :*Golden Roof*Kaiserliche Hofburg *Hofkirche with the cenotaph of Maximilian I, Holy Roman Emperor*Altes Landhaus...
, Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
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
Trieste is a city and seaport in northeastern Italy. It is situated towards the end of a narrow strip of land lying between the Adriatic Sea and Italy's border with Slovenia, which lies almost immediately south and east of the city...
insurance company Assicurazioni Generali
Assicurazioni Generali
Assicurazioni Generali S.p.A. is the largest insurance company in Italy and one of the largest in Europe. It has its headquarters in Trieste...
.
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 in Padua and then 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
Frank P. Ramsey
Frank Plumpton Ramsey was a British mathematician who, in addition to mathematics, made significant and precocious contributions in philosophy and economics before his death at the age of 26...
. 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 only became known in the Anglo-American statistical world in the 1950s when L. J. Savage, who had independently adopted subjectivism
Bayesian inference
In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...
, drew him into it; another great champion was Dennis Lindley
Dennis Lindley
Dennis Victor Lindley is a British statistician, decision theorist and leading advocate of Bayesian statistics.Dennis Lindley grew up in the south-west London suburb of Surbiton. He was an only child and his father was a local building contractor...
. De Finetti died in Rome
Rome
Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
.
Work
De Finetti emphasized a predictive inferencePredictive inference
Predictive inference is an approach to statistical inference that emphasizes the prediction of future observations based on past observations.Initially, predictive inference was based on observable parameters and it was the main purpose of studying probability, but it fell out of favor in the 20th...
approach to statistics;
he proposed a thought experiment
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...
along the following lines (described in greater detail at coherence (philosophical gambling strategy)
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 on which he is wagering, even if his opponent makes...
): 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
Odds
The odds in favor of an event or a proposition are expressed as the ratio of a pair of integers, which is the ratio of the probability that an event will happen to the probability that it will not happen...
, that do not expose you to certain loss through a Dutch book
Dutch book
In gambling a Dutch book or lock is a set of odds and bets which guarantees a profit, regardless of the outcome of the gamble. It is associated with probabilities implied by the odds not being coherent....
are called coherent.
De Finetti is also noted for de Finetti's theorem
De Finetti's theorem
In probability theory, de Finetti's theorem explains why exchangeable observations are conditionally independent given some latent variable to which an epistemic probability distribution would then be assigned...
on exchangeable
De Finetti's theorem
In probability theory, de Finetti's theorem explains why exchangeable observations are conditionally independent given some latent variable to which an epistemic probability distribution would then be assigned...
sequences of random variable
Random variable
In probability and statistics, a random variable or stochastic variable is, roughly speaking, a variable whose value results from a measurement on some type of random process. Formally, it is a function from a probability space, typically to the real numbers, which is measurable functionmeasurable...
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
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 and is used to graph the genotype frequencies of populations, where there are two alleles and the population is diploid...
s for graphing genotype
Genotype
The genotype is the genetic makeup of a cell, an organism, or an individual usually with reference to a specific character under consideration...
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.
The de Finetti Award, presented annually by the European Association for Decision Making, is named after him.
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.
- 1937, “La Prévision: ses lois logiques, ses sources subjectives,” Annales de l'Institut Henri Poincaré,
- - "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 by A Machi and AFM Smith of 1970 book) 2 volumes, New York: Wiley, 1974-5.
Discussions
- D. V. LindleyDennis LindleyDennis Victor Lindley is a British statistician, decision theorist and leading advocate of Bayesian statistics.Dennis Lindley grew up in the south-west London suburb of Surbiton. He was an only child and his father was a local building contractor...
, "Bruno de Finetti, 1906-1985 (Obituary)" Journal of the Royal Statistical SocietyJournal of the Royal Statistical SocietyThe Journal of the Royal Statistical Society is a series of three peer-reviewed statistics journals published by Blackwell Publishing for the London-based Royal Statistical Society.- History :...
, 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
- Coherence (philosophical gambling strategy)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 on which he is wagering, even if his opponent makes...
- De Finetti diagramDe Finetti diagramA de Finetti diagram is a ternary plot used in population genetics. It is named after the Italian statistician Bruno de Finetti and is used to graph the genotype frequencies of populations, where there are two alleles and the population is diploid...
- De Finetti's theoremDe Finetti's theoremIn probability theory, de Finetti's theorem explains why exchangeable observations are conditionally independent given some latent variable to which an epistemic probability distribution would then be assigned...
- Exchangeability
- Infinitely divisible probability distributions
- Predictive inferencePredictive inferencePredictive inference is an approach to statistical inference that emphasizes the prediction of future observations based on past observations.Initially, predictive inference was based on observable parameters and it was the main purpose of studying probability, but it fell out of favor in the 20th...
- Quasiconvex functionQuasiconvex functionIn 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 is a convex set...
External links
- Probabilità e induzione, Bologna, 1993.
- Bruno de Finetti website
- Generate finetti diagrams online
- MacTutor: Bruno de Finetti
- Bruno De Finetti Finding Aid at the University of Pittsburgh's Archive of Scientific Philosophy
- De Finetti on the Portraits of Statisticians page.
- Interpretations of Probability from 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
