Bayesian regret: Difference between revisions
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This term has been used to compare a random buy-and-hold strategy to professional traders' records. This same concept has received numerous different names, as the New York Times notes: |
This term has been used to compare a random buy-and-hold strategy to professional traders' records. This same concept has received numerous different names, as the New York Times notes: |
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"In 1957, for example, a statistician named James Hanna called his theorem Bayesian Regret. He had been preceded by [[David Blackwell]], also a statistician, who called his theorem Controlled Random Walks.<ref>Controlled random walks, D Blackwell, Proceedings of the International Congress of Mathematicians 3, 336-338</ref> Other, later papers had titles like 'On Pseudo Games',<ref>{{Cite journal |last=Banos |first=Alfredo |date=December 1968 |title=On Pseudo-Games |url=https://projecteuclid.org/journals/annals-of-mathematical-statistics/volume-39/issue-6/On-Pseudo-Games/10.1214/aoms/1177698023.full |journal=The Annals of Mathematical Statistics |volume=39 |issue=6 |pages=1932–1945 |doi=10.1214/aoms/1177698023 |issn=0003-4851}}</ref> 'How to Play an Unknown Game'{{Citation needed|date=June 2023}}, 'Universal Coding'<ref>{{Cite journal |last=Rissanen |first=J. |date=July 1984 |title=Universal coding, information, prediction, and estimation |url=https://ieeexplore.ieee.org/abstract/document/1056936 |journal=IEEE Transactions on Information Theory |volume=30 |issue=4 |pages=629–636 |doi=10.1109/TIT.1984.1056936 |issn=1557-9654}}</ref> and 'Universal Portfolios'".<ref>{{Cite journal |last=Cover |first=Thomas M. |date=January 1991 |title=Universal Portfolios |url=https://onlinelibrary.wiley.com/doi/10.1111/j.1467-9965.1991.tb00002.x |journal=Mathematical Finance |language=en |volume=1 |issue=1 |pages=1–29 |doi=10.1111/j.1467-9965.1991.tb00002.x |issn=0960-1627}}</ref><ref>{{Cite news|url=https://www.nytimes.com/2006/02/05/weekinreview/pity-the-scientist-who-discovers-the-discovered.html|title=Pity the Scientist Who Discovers the Discovered|last=Kolata|first=Gina|date=2006-02-05|work=The New York Times|access-date=2017-02-27|issn=0362-4331}}</ref> |
"In 1957, for example, a statistician named James Hanna called his theorem Bayesian Regret. He had been preceded by [[David Blackwell]], also a statistician, who called his theorem Controlled Random Walks.<ref>Controlled random walks, D Blackwell, Proceedings of the International Congress of Mathematicians 3, 336-338</ref> Other, later papers had titles like 'On Pseudo Games',<ref>{{Cite journal |last=Banos |first=Alfredo |date=December 1968 |title=On Pseudo-Games |url=https://projecteuclid.org/journals/annals-of-mathematical-statistics/volume-39/issue-6/On-Pseudo-Games/10.1214/aoms/1177698023.full |journal=The Annals of Mathematical Statistics |volume=39 |issue=6 |pages=1932–1945 |doi=10.1214/aoms/1177698023 |issn=0003-4851}}</ref> 'How to Play an Unknown Game'<ref>{{Citation |last=Harsanyi |first=John C. |title=Games with Incomplete Information Played by “Bayesian” Players, I–III Part I. The Basic Model |date=1982 |url=http://dx.doi.org/10.1007/978-94-017-2527-9_6 |work=Papers in Game Theory |pages=115–138 |access-date=2023-06-13 |place=Dordrecht |publisher=Springer Netherlands |isbn=978-90-481-8369-2}}</ref>{{Citation needed|date=June 2023}}, 'Universal Coding'<ref>{{Cite journal |last=Rissanen |first=J. |date=July 1984 |title=Universal coding, information, prediction, and estimation |url=https://ieeexplore.ieee.org/abstract/document/1056936 |journal=IEEE Transactions on Information Theory |volume=30 |issue=4 |pages=629–636 |doi=10.1109/TIT.1984.1056936 |issn=1557-9654}}</ref> and 'Universal Portfolios'".<ref>{{Cite journal |last=Cover |first=Thomas M. |date=January 1991 |title=Universal Portfolios |url=https://onlinelibrary.wiley.com/doi/10.1111/j.1467-9965.1991.tb00002.x |journal=Mathematical Finance |language=en |volume=1 |issue=1 |pages=1–29 |doi=10.1111/j.1467-9965.1991.tb00002.x |issn=0960-1627}}</ref><ref>{{Cite news|url=https://www.nytimes.com/2006/02/05/weekinreview/pity-the-scientist-who-discovers-the-discovered.html|title=Pity the Scientist Who Discovers the Discovered|last=Kolata|first=Gina|date=2006-02-05|work=The New York Times|access-date=2017-02-27|issn=0362-4331}}</ref> |
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==Social Choice (voting methods)== |
==Social Choice (voting methods)== |
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Revision as of 06:00, 13 June 2023
 | This article includes a list of general references, but it lacks sufficient corresponding inline citations. (May 2021) |
In stochastic game theory, Bayesian regret is the expected difference ("regret") between the utility of a Bayesian strategy and that of the optimal strategy (the one with the highest expected payoff).
The term Bayesian refers to Thomas Bayes (1702–1761), who proved a special case of what is now called Bayes' theorem, who provided the first mathematical treatment of a non-trivial problem of statistical data analysis using what is now known as Bayesian inference.
Economics
This term has been used to compare a random buy-and-hold strategy to professional traders' records. This same concept has received numerous different names, as the New York Times notes:
"In 1957, for example, a statistician named James Hanna called his theorem Bayesian Regret. He had been preceded by David Blackwell, also a statistician, who called his theorem Controlled Random Walks.[1] Other, later papers had titles like 'On Pseudo Games',[2] 'How to Play an Unknown Game'[3][citation needed], 'Universal Coding'[4] and 'Universal Portfolios'".[5][6]
Social Choice (voting methods)
"Bayesian Regret" has also been used as an alternate term for social utility efficiency, that is, a measure of the expected utility of different voting methods under a given probabilistic model of voter utilities and strategies. In this case, the relation to Bayes is unclear, as there is no conditioning or posterior distribution involved.
References
 | This article has an unclear citation style. (September 2018) |
- ^ Controlled random walks, D Blackwell, Proceedings of the International Congress of Mathematicians 3, 336-338
- ^ Banos, Alfredo (December 1968). "On Pseudo-Games". The Annals of Mathematical Statistics. 39 (6): 1932–1945. doi:10.1214/aoms/1177698023. ISSN 0003-4851.
- ^ Harsanyi, John C. (1982), "Games with Incomplete Information Played by "Bayesian" Players, I–III Part I. The Basic Model", Papers in Game Theory, Dordrecht: Springer Netherlands, pp. 115–138, ISBN 978-90-481-8369-2, retrieved 2023-06-13
- ^ Rissanen, J. (July 1984). "Universal coding, information, prediction, and estimation". IEEE Transactions on Information Theory. 30 (4): 629–636. doi:10.1109/TIT.1984.1056936. ISSN 1557-9654.
- ^ Cover, Thomas M. (January 1991). "Universal Portfolios". Mathematical Finance. 1 (1): 1–29. doi:10.1111/j.1467-9965.1991.tb00002.x. ISSN 0960-1627.
- ^ Kolata, Gina (2006-02-05). "Pity the Scientist Who Discovers the Discovered". The New York Times. ISSN 0362-4331. Retrieved 2017-02-27.