Posterior odds on a model

A way to check among models which one has the best odds of being right. Note this is just a meta version of Bayes Theorem

• - Probability of model j being “the best” among all the choices
• - The likelihood of the data under model j
• - Prior beliefs about the probability of model j being the best
• - This is a weighted average of the likelihoods of the data under each model with the prior probabilities as weights - basically the expected value of the model mixture

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References

@lancaster2004 - chapter 2