Bayesian model selection - Revision history

DavidB4-bot: /* top */clean up & uniformity

2016-07-13T02:59:49Z

top: clean up & uniformity

RJJensen at 21:14, November 8, 2009

2009-11-08T21:14:34Z

Qwestor at 15:11, January 17, 2009

2009-01-17T15:11:48Z

Ed Poor: still don't get it - can't you write this in simpler terms?

2008-01-02T01:20:26Z

still don't get it - can't you write this in simpler terms?

Ed Poor at 01:19, January 2, 2008

2008-01-02T01:19:51Z

Qwestor at 17:34, December 28, 2007

2007-12-28T17:34:45Z

Qwestor at 14:27, December 27, 2007

2007-12-27T14:27:31Z

Qwestor at 16:22, December 8, 2007

2007-12-08T16:22:38Z

Qwestor at 15:35, December 8, 2007

2007-12-08T15:35:51Z

Qwestor at 14:14, December 8, 2007

2007-12-08T14:14:57Z

← Older revision		Revision as of 02:59, July 13, 2016
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−	[[~~category~~:Probability and Statistics]]	+	[[Category:Probability and Statistics]]

← Older revision		Revision as of 21:14, November 8, 2009
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−	[[category:Probability]]	+	[[category:Probability and Statistics]]

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 In [[Bayesian Probability]], '''Bayesian model selection''' is a method for choosing the best [[hypothesis]] or ''model class'' or [[mathematical model]] posed as a [[probabilistic likelihood model]] out of a set of competing model classes (loosely ''models'') which best explains some observed data. Best here is measured by the [[Bayesian posterior]] [[Bayes odds|odds]] ratio of the winner compared against all other candidates in the competition.
-The posterior [[Bayes odds|odds]] ratio is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio. In short one is comparing the [[marginal likelihood]] of entire families of models (i.e., parameterized model classes) by marginalizing over their associated parameter values.  After the model class has been so selected, one can then go on to do [[parameter estimation]] to determine the best inference as to the values of the parameters of that particular model class.
+The posterior [[Bayes odds|odds]] ratio is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio. In short one is comparing the [[marginal likelihood]] of entire families of models (i.e., parameterized model classes) by [[marginal distribution|marginalizing]] over their associated parameter values.  After the model class has been so selected, one can then go on to do [[parameter estimation]] to determine the best inference as to the values of the parameters of that particular model class.
 [[category:Probability]]

@@ Line 1: / Line 1: @@
 In [[Bayesian Probability]], '''Bayesian model selection''' is a method for choosing the best [[hypothesis]] or ''model class'' or [[mathematical model]] posed as a [[probabilistic likelihood model]] out of a set of competing model classes (loosely ''models'') which best explains some observed data. Best here is measured by the [[Bayesian posterior]] [[Bayes odds|odds]] ratio of the winner compared against all other candidates in the competition.
-The posterior [[Bayes odds|odds]] ratio is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio. In short one is comparing the [[marginal likelihood]] of entire families of models (i.e., parameterized model classes) by marginalizing over their assocaited parameter values.  After the model class has been so selected, one can then go on to do [[parameter estimation]] to determine the best inference as to the values of the parameters of that particular model class.
+The posterior [[Bayes odds|odds]] ratio is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio. In short one is comparing the [[marginal likelihood]] of entire families of models (i.e., parameterized model classes) by marginalizing over their associated parameter values.  After the model class has been so selected, one can then go on to do [[parameter estimation]] to determine the best inference as to the values of the parameters of that particular model class.
 [[category:Probability]]

← Older revision		Revision as of 01:19, January 2, 2008
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−	In [[Bayesian Probability]], '''Bayesian model selection''' is a method for choosing the best [[hypothesis]] or ''model class'' or [[mathematical model]] posed as a [[probabilistic likelihood model]] out of a set of competing model classes (loosely ''models'') which best explains some observed data. Best here is measured by the [[Bayesian posterior]] [[Bayes odds\|odds]] ratio of the winner compared against all other candidates in the competition. The posterior [[Bayes odds\|odds]] ratio is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio. In short one is comparing the [[marginal likelihood]] of entire families of models (i.e., parameterized model classes) by marginalizing over their assocaited parameter values. After the model class has been so selected, one can then go on to do [[parameter estimation]] to determine the best inference as to the values of the parameters of that particular model class.	+	In [[Bayesian Probability]], '''Bayesian model selection''' is a method for choosing the best [[hypothesis]] or ''model class'' or [[mathematical model]] posed as a [[probabilistic likelihood model]] out of a set of competing model classes (loosely ''models'') which best explains some observed data. Best here is measured by the [[Bayesian posterior]] [[Bayes odds\|odds]] ratio of the winner compared against all other candidates in the competition.
		+
		+	The posterior [[Bayes odds\|odds]] ratio is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio. In short one is comparing the [[marginal likelihood]] of entire families of models (i.e., parameterized model classes) by marginalizing over their assocaited parameter values. After the model class has been so selected, one can then go on to do [[parameter estimation]] to determine the best inference as to the values of the parameters of that particular model class.


	[[category:Probability]]		[[category:Probability]]

← Older revision		Revision as of 17:34, December 28, 2007
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−	In [[Bayesian Probability]], '''Bayesian model selection''' is a method for choosing the best [[hypothesis]] or [[model ~~class~~]] posed as a [[probabilistic likelihood model]] out of a set of competing model classes which best explains some observed data. Best here is measured by the [[Bayesian posterior odds]] ratio of the winner compared against all other candidates in the competition. The ~~'''~~posterior odds ratio~~'''~~ is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio. In short one is comparing the [[marginal likelihood]] of entire classes by marginalizing over their assocaited parameter values. After the model class has been so selected, one can then go on to do [[parameter estimation]] to determine the best inference as to the values of the parameters of that particular model class.	+	In [[Bayesian Probability]], '''Bayesian model selection''' is a method for choosing the best [[hypothesis]] or ''model class'' or [[mathematical model]] posed as a [[probabilistic likelihood model]] out of a set of competing model classes (loosely ''models'') which best explains some observed data. Best here is measured by the [[Bayesian posterior]] [[Bayes odds\|odds]] ratio of the winner compared against all other candidates in the competition. The posterior [[Bayes odds\|odds]] ratio is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio. In short one is comparing the [[marginal likelihood]] of entire families of models (i.e., parameterized model classes) by marginalizing over their assocaited parameter values. After the model class has been so selected, one can then go on to do [[parameter estimation]] to determine the best inference as to the values of the parameters of that particular model class.


	[[category:Probability]]		[[category:Probability]]

← Older revision		Revision as of 14:27, December 27, 2007
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−	In [[Bayesian Probability]], '''Bayesian model selection''' is a method for choosing the best [[hypothesis]] posed as a [[probabilistic likelihood model]] out of a set of competing ~~models~~ which best explains some observed data. Best here is measured by the [[Bayesian posterior odds]] ratio of the winner compared against all other candidates in the competition. The '''posterior odds ratio''' is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio.	+	In [[Bayesian Probability]], '''Bayesian model selection''' is a method for choosing the best [[hypothesis]] or [[model class]] posed as a [[probabilistic likelihood model]] out of a set of competing model classes which best explains some observed data. Best here is measured by the [[Bayesian posterior odds]] ratio of the winner compared against all other candidates in the competition. The '''posterior odds ratio''' is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio. In short one is comparing the [[marginal likelihood]] of entire classes by marginalizing over their assocaited parameter values. After the model class has been so selected, one can then go on to do [[parameter estimation]] to determine the best inference as to the values of the parameters of that particular model class.


	[[category:Probability]]		[[category:Probability]]

← Older revision		Revision as of 16:22, December 8, 2007
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−	In [[Bayesian Probability]], '''Bayesian model selection''' is a method for choosing the best [[hypothesis]] (model) out of a set of competing models which best explains some observed data. Best here is measured by the [[Bayesian posterior odds]] ratio of the winner compared against all other candidates in the competition. The '''posterior odds ratio''' is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio.	+	In [[Bayesian Probability]], '''Bayesian model selection''' is a method for choosing the best [[hypothesis]] posed as a [[probabilistic likelihood model]] out of a set of competing models which best explains some observed data. Best here is measured by the [[Bayesian posterior odds]] ratio of the winner compared against all other candidates in the competition. The '''posterior odds ratio''' is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio.


	[[category:Probability]]		[[category:Probability]]

← Older revision		Revision as of 15:35, December 8, 2007
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−	[[category:~~statistics~~]]	+	[[category:Probability]]

← Older revision		Revision as of 14:14, December 8, 2007
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−	'''Bayesian model selection''' is a ~~technique in probability theory~~ for choosing a [[hypothesis]] (model) ~~to fit~~ observed data.	+	In [[Bayesian Probability]], '''Bayesian model selection''' is a method for choosing the best [[hypothesis]] (model) out of a set of competing models which best explains some observed data. Best here is measured by the [[Bayesian posterior odds]] ratio of the winner compared against all other candidates in the competition. The '''posterior odds ratio''' is the product of the [[Bayes Factor]] and the [[Bayes prior]] odds ratio.
		+

−	~~The model selection implicitly prefers simpler models, and it ensures that the right model, if it exists, will be selected as the size of the dataset increases to infinity.~~
	[[category:statistics]]		[[category:statistics]]