Bayesian regret
{{More footnotes needed|date=May 2021}}
In stochastic game theory, Bayesian regret is the expected difference ("regret") between the utility of a given strategy and the utility of the best possible strategy in hindsight—i.e., the strategy that would have maximized expected payoff if the true underlying model or distribution were known. This notion of regret measures how much is lost, on average, due to uncertainty or imperfect information.
Etymology
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.Controlled random walks, D Blackwell, Proceedings of the International Congress of Mathematicians 3, 336-338 Other, later papers had titles like 'On Pseudo Games',{{Cite journal |last=Banos |first=Alfredo |date=December 1968 |title=On Pseudo-Games |journal=The Annals of Mathematical Statistics |volume=39 |issue=6 |pages=1932–1945 |doi=10.1214/aoms/1177698023 |issn=0003-4851|doi-access=free }} 'How to Play an Unknown Game'{{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 |doi=10.1007/978-94-017-2527-9_6 |isbn=978-90-481-8369-2|url-access=subscription }}{{Citation needed|date=June 2023}}, 'Universal Coding'{{Cite journal |last=Rissanen |first=J. |date=July 1984 |title=Universal coding, information, prediction, and estimation |url=https://ieeexplore.ieee.org/document/1056936 |journal=IEEE Transactions on Information Theory |volume=30 |issue=4 |pages=629–636 |doi=10.1109/TIT.1984.1056936 |s2cid=206735464 |issn=1557-9654|url-access=subscription }} and 'Universal Portfolios'".{{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 |s2cid=219967240 |issn=0960-1627|url-access=subscription }}{{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}}
References
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