Bayesian model selection

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 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 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.