Bruno de Finetti

Bruno De Finetti
Bruno de Finetti portrait.jpg
Born(1906-06-13)13 June 1906
Died20 July 1985(1985-07-20) (aged 79)
Rome, Italy
NationalityItalian
Alma materPolitecnico di Milano
Scientific career
FieldsMathematics
InfluencesGiulio Vivanti

Bruno de Finetti (13 June 1906 – 20 July 1985) 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,"[1] which discussed probability founded on the coherence of betting odds and the consequences of exchangeability.

Life

De Finetti was born in Innsbruck, 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 Istituto Nazionale di Statistica (National Institute of Statistics) in Rome and, from 1931, the 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;[2] 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 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.[3] De Finetti held different social and political beliefs through his life: following Fascism during his youth, then moving to Christian socialism and finally adhering to the Radical Party.[2][4]

드 피네티는 1950년대에 독립적으로 주관주의를 채택했던 L. J. 새비지가 그를 끌어들이면서 영미 통계계에 알려지게 되었다. 또 다른 위대한 챔피언은 데니스 린들리였다. 드 피네티는 1985년 로마에서 죽었다.

작업 및 영향

De Finetti는 통계에 대한 예측 추론 접근법을 강조했다. 그는 다음과 같은 노선을 따라 사고 실험을 제안했다(철학적 도박 전략에서 더 자세히 설명됨). 10억년 전 화성에 생명체가 있었다면 1달러, 없으면 0달러의 약속 가격을 정해야 하고, 내일이면 답이 공개된다. 상대가 당신이 정한 가격으로 당신에게서 그런 약속을 살 것인지 아니면 여전히 같은 가격으로 상대에게 그런 약속을 살 것을 요구할 것인지 선택할 수 있다는 것을 알고 있을 것이다. 즉, 승산은 당신이 정하지만, 상대가 내기의 어느 쪽이 당신의 것이 될지를 결정한다. 당신이 설정한 가격은 당신이 베팅하고 있는 제안에 할당하는 "운영적 주관적 확률"이다. 이 가격은 1달러(또는 마이너스 가격) 이상의 가격을 설정할 때처럼 특정 손실에 직면하지 않을 경우 확률 공리를 따라야 한다. 디 피네티는 둘 이상의 사건에 대한 내기를 고려함으로써 긍정을 정당화할 수 있었다. 네덜란드어 책을 통해 당신을 특정한 손실에 노출시키지 않는 가격, 즉 동등하게 승산이 있는 것을 일관성이라고 부른다.

De Finetti는 또한 랜덤 변수의 교환 가능한 시퀀스에 대한 De Finetti의 정리로도 유명하다. De Finetti는 교환성을 연구한 첫 번째 사람은 아니었지만 그는 그 주제를 더 잘 보이게 했다. 그는 1920년대 후반부터 교환가능성에 대해 출판하기 시작했지만 1937년 기사는 그의 가장 유명한 치료법이다.

1929년 데 피네티는 무한히 분리할 수 있는 확률 분포의 개념을 도입했다.

그는 유전자형 주파수를 그래프로 표시하는 데 피네티 도표도 소개했다.

1974년 그의 책을 영어로 번역한 것은 앵글로폰 세계의 예측 추론에 대한 관심을 되살리고, 교환가능성에 대한 생각을 관심을 환기시킨 공로를 인정받고 있다.[5]

In 1961 he was elected as a Fellow of the American Statistical Association.[6] 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 21'st century quantum extensions of de Finetti's representation theorem have been found to be useful in quantum information,[7][8][9] in topics like quantum key distribution[10] and entanglement detection.[11]

Bibliography

See Works on

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 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, 1974–1975.

Discussions

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

References

  1. ^ "La prévision: ses lois logiques, ses sources subjectives," Annales de l'Institut Henri Poincaré, 7, 1-68,
  2. ^ a b "Guide to the Bruno De Finetti Papers, 1924-2000 ASP.1992.01 Digital Pitt". digital.library.pitt.edu. Retrieved 2019-05-01.
  3. ^ A Conversation with Eugenio Ragazzini, Statistical Science, 2011
  4. ^ Prünster, Igor; Lijoi, Antonio (November 2011). "A Conversation with Eugenio Regazzini". Statistical Science. 26 (4): 647–672. arXiv:1205.4807. doi:10.1214/11-STS362. ISSN 0883-4237. S2CID 53383544.
  5. ^ Predictive Inference: An Introduction, Seymour Geisser, CRC Press, 1993 ISBN 0-412-03471-9
  6. ^ View/Search Fellows of the ASA, accessed 2016-07-23.
  7. ^ Caves, Carlton M.; Fuchs, Christopher A.; Schack, Ruediger (2002-08-20). "Unknown quantum states: The quantum de Finetti representation". Journal of Mathematical Physics. 43 (9): 4537–4559. arXiv:quant-ph/0104088. Bibcode:2002JMP....43.4537C. doi:10.1063/1.1494475. ISSN 0022-2488. S2CID 17416262.
  8. ^ J. Baez (2007). "This Week's Finds in Mathematical Physics (Week 251)". Retrieved 29 April 2012.
  9. ^ Brandao, Fernando G.S.L.; Harrow, Aram W. (2013-01-01). "Quantum De Finetti Theorems Under Local Measurements with Applications". Proceedings of the Forty-fifth Annual ACM Symposium on Theory of Computing. STOC '13. New York, NY, USA: ACM: 861–870. arXiv:1210.6367. doi:10.1145/2488608.2488718. ISBN 9781450320290. S2CID 1772280.
  10. ^ Renner, Renato (2005-12-30). "Security of Quantum Key Distribution". arXiv:quant-ph/0512258. Bibcode:2005PhDT.......176R. Cite journal requires journal= (help)
  11. ^ Doherty, Andrew C.; Parrilo, Pablo A.; Spedalieri, Federico M. (2005-01-01). "Detecting multipartite entanglement". Physical Review A. 71 (3): 032333. arXiv:quant-ph/0407143. Bibcode:2005PhRvA..71c2333D. doi:10.1103/PhysRevA.71.032333. S2CID 44241800.

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