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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]] 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 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.  

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:statistics]]

 

 

[[Category:Probability and Statistics]]