Conditional random field

Template:Noref 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 ${\delta }_1$ and ${\delta }_2$ be two decision rules, and let $R(\theta ,\delta )$ be the risk of rule $\delta$ for parameter $\theta$. The decision rule ${\delta }_1$ is said to dominate the rule ${\delta }_2$ if $R(\theta ,{\delta }_1)\le R(\theta ,{\delta }_2)$ for all $\theta$, and the inequality is strict for some $\theta$.

This defines a partial order on decision rules; the maximal elements with respect to this order are called admissible decision rules.

See also

• Admissible decision rule

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