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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. The references used may be made clearer with a different or consistent style of citation and footnoting. (September 2018) (Learn how and when to remove this template message)
  1. ^ Controlled random walks, D Blackwell, Proceedings of the International Congress of Mathematicians 3, 336-338
  2. ^ Banos, Alfredo (December 1968). "On Pseudo-Games". The Annals of Mathematical Statistics. 39 (6): 1932–1945. doi:10.1214/aoms/1177698023. ISSN 0003-4851.
  3. ^ 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, doi:10.1007/978-94-017-2527-9_6, ISBN 978-90-481-8369-2, retrieved 2023-06-13
  4. ^ 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. S2CID 206735464.
  5. ^ 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. S2CID 219967240.
  6. ^ Kolata, Gina (2006-02-05). "Pity the Scientist Who Discovers the Discovered". The New York Times. ISSN 0362-4331. Retrieved 2017-02-27.
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