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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 order to evaluate the usefulness of a decision rule, it is necessary to have a loss function detailing the outcome of each action under different states.
In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function.
An estimation procedure that is often claimed to be part of Bayesian statistics is the maximum a posteriori (MAP) estimate of an unknown quantity, that equals the mode of the posterior density with respect to some reference measure, typically the Lebesgue measure.
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).
The likelihood-ratio test provides the decision rule as follows: ... determined then it can directly be used to form decision regions (to sustain or reject the null ...
In the latter equation, the integrand inside dx is known as the Posterior Risk, and minimising it with respect to decision a also minimizes the overall Bayes Risk. This optimal decision, a * is known as the Bayes (decision) Rule - it minimises the average loss over all possible states of nature θ, over all possible (probability-weighted) data ...
“Financial education may help people retain sharp decision-making abilities on the money front,” the study said. ... Another important figure to calculate is how much you need to retire. You ...
An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. It is an important concept in decision theory . In order to compare the different decision outcomes, one commonly assigns a utility value to each of them.