In the statistical
decision theory
Decision theory or the theory of rational choice is a branch of probability theory, probability, economics, and analytic philosophy that uses expected utility and probabilities, probability to model how individuals would behave Rationality, ratio ...
, where one is faced with making decisions in the presence of statistical knowledge, Γ-minimax inference is a
minimax
Minimax (sometimes Minmax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, combinatorial game theory, statistics, and philosophy for ''minimizing'' the possible loss function, loss for a Worst-case scenari ...
approach used to deal with partial prior information. It works with applications of Γ-minimax to statistical estimation, and contains Γ-minimax theory, used to pick applicable decision rules to use when given partial prior information about the distribution of an unknown parameter. The decision rule selected must be the one that minimizes the supremum of the payoff over the priors in Γ, with Bayes and regret risk prioritized in a frequentist approach, and posterior expected loss and regret prioritized in a Bayesian one.
History
The Γ-minimax principle has been discussed and proposed before by
Herbert Robbins
Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician. He did research in topology, measure theory, statistics, and a variety of other fields.
He was the co-author, with Richard Courant ...
. and
I. J. Good to deal with instances of partial prior information that can arise from the minimax approach pioneered by
Abraham Wald
Abraham Wald (; ; , ; – ) was a Hungarian and American mathematician and statistician who contributed to decision theory, geometry and econometrics, and founded the field of sequential analysis. One of his well-known statistical works was ...
.
[Wald, A. (1950). ''Statistical Decision Functions.'' Wiley, New York]
References
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Decision theory