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Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses the tools of expected utility and probability to model how individuals would behave rationally under uncertainty.
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.
Lucien Le Cam credits him in his own book, Asymptotic Methods in Statistical Decision Theory: "The ideas and techniques used reflect first and foremost the influence of Abraham Wald's writings." [12] He is the father of the noted American physicist Robert Wald.
He was an influential Bayesian decision theorist and pioneer in the field of decision analysis, with works in statistical decision theory, game theory, behavioral decision theory, risk analysis, and negotiation analysis. [2] He helped found and was the first director of the International Institute for Applied Systems Analysis. [3] [4]
In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always "better" than it [1] (or at least sometimes better and never worse), in the precise sense of "better" defined below.
Statistics subsequently branched out into various directions, including decision theory, Bayesian statistics, exploratory data analysis, robust statistics, and non-parametric statistics. Neyman-Pearson hypothesis testing made significant contributions to decision theory, which is widely employed, particularly in statistical quality control.
His courses on statistical decision theory taught at Carnegie-Mellon influenced Edward C. Prescott and Robert Lucas, Jr., [4] influential figures in the development of new classical macroeconomics and real business-cycle theory. DeGroot's undergraduate text, Probability and Statistics, published in 1975, is widely recognized as a classic textbook.
With the establishment of modern decision theory in the 1950s, the model became a key ingredient in the formulation of non-probabilistic decision-making models in the face of severe uncertainty. [ 4 ] [ 5 ] It is widely used in diverse fields such as decision theory , control theory , economics , statistics , robust optimization , operations ...