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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 .
In statistical decision theory, a randomised decision rule or mixed decision rule is a decision rule that associates probabilities with deterministic decision rules. In finite decision problems, randomised decision rules define a risk set which is the convex hull of the risk points of the nonrandomised decision rules.
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.
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.
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 weighted average rule gives different weights to different voters (for example, based on their level of expertise). The trimmed average rule discards some of the extreme bids, and returns the average of the remaining bids. Renault and Trannoy study the combined use of the average rule and the majority rule, and their effect on minority ...
To demonstrate the unintuitive nature of Stein's example, consider the following real-world example. Suppose we are to estimate three unrelated parameters, such as the US wheat yield for 1993, the number of spectators at the Wimbledon tennis tournament in 2001, and the weight of a randomly chosen candy bar from the supermarket.
Consensus is not synonymous with unanimity – though that may be a rule agreed to in a specific decision-making process. The level of agreement necessary to finalize a decision is known as a decision rule. [17] [21] Diversity of opinion is normal in most all situations, and will be represented proportionately in an appropriately functioning group.