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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 [[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]]
[[Category:Probability and Statistics]]