stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...

game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

, 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 In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For examp ...

, who provided the first mathematical treatment of a non-trivial problem of statistical data analysis using what is now known as

Bayesian inference Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, a ...

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. Other, later papers had titles like 'On Pseudo Games', 'How to Play an Unknown Game', 'Universal Coding' and 'Universal Portfolios'".

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

{{Reflist Game theory Bayesian estimation Economic theories Machine learning Bayesian statistics Social choice theory