Conditional random field - Revision history

en>Velvel2: /* See also */ fundamental theorem

2014-12-15T09:01:39Z

See also: fundamental theorem

← Older revision		Revision as of 11:01, 15 December 2014
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	~~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]~~]

en>Qwertyus: /* References */ reflist

2013-12-24T14:26:42Z

References: reflist

← Older revision		Revision as of 16:26, 24 December 2013
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			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]]

111.193.180.199: /* Software */

2012-08-16T15:19:36Z

Software

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