Changes

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.   

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]]

[[category:Probability]]