Conditional random field: Difference between revisions

Revision as of 15:26, 24 December 2013

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 $δ_{1}$ and $δ_{2}$ be two decision rules, and let $R (θ, δ)$ be the risk of rule $δ$ for parameter $θ$ . The decision rule $δ_{1}$ is said to dominate the rule $δ_{2}$ if $R (θ, δ_{1}) \leq R (θ, δ_{2})$ for all $θ$ , and the inequality is strict for some $θ$ .

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

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+{{Noref|date=July 2010}}
+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 <math>\delta_1</math> and <math>\delta_2</math> be two [[decision theory|decision rules]], and let <math>R(\theta, \delta)</math> be the [[risk function|risk]] of rule <math>\delta</math> for parameter <math>\theta</math>. The decision rule <math>\delta_1</math> is said to dominate the rule <math>\delta_2</math> if <math>R(\theta,\delta_1)\le R(\theta,\delta_2)</math> for all <math>\theta</math>, and the inequality is strict for some <math>\theta</math>.
+This defines a [[partial order]] on decision rules; the [[maximal element]]s with respect to this order are called ''[[admissible decision rule]]s.''
+== See also ==
+* [[Admissible decision rule]]
+{{statistics-stub}}
+[[Category:Decision theory]]

Conditional random field: Difference between revisions

Revision as of 15:26, 24 December 2013

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