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In decision theory, a decision rule is a function which maps an observation to an appropriate action. Decision rules play an important role in the theory of statistics and economics , and are closely related to the concept of a strategy in game theory .
As with nonrandomised decision rules, randomised decision rules may satisfy favourable properties such as admissibility, minimaxity and Bayes. This shall be illustrated in the case of a finite decision problem, i.e. a problem where the parameter space is a finite set of, say, elements.
A decision rule that minimizes (,) is called a Bayes rule with respect to (). There may be more than one such Bayes rule. There may be more than one such Bayes rule. If the Bayes risk is infinite for all δ {\displaystyle \delta \,\!} , then no Bayes rule is defined.
In decision theory, a decision rule is said to dominate another if the performance of the former is sometimes better, and never worse, than that of the latter. Formally, let δ 1 {\displaystyle \delta _{1}} and δ 2 {\displaystyle \delta _{2}} be two decision rules , and let R ( θ , δ ) {\displaystyle R(\theta ,\delta )} be the risk of rule ...
The mythological Judgement of Paris required selecting from three incomparable alternatives (the goddesses shown).. 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.
Admissible decision rule; Age adjustment; Age-standardized mortality rate; Age stratification; Aggregate data; Aggregate pattern; Akaike information criterion; Algebra of random variables; Algebraic statistics; Algorithmic inference; Algorithms for calculating variance; All models are wrong; All-pairs testing; Allan variance; Alignments of ...
An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an objective property of an estimator. Bias is a distinct concept from consistency : consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased (see bias versus consistency for more).
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