5.9 Summary

In this chapter, we have seen how to compare models using posterior predictive checks, information criteria, approximated cross-validation, and Bayes factors.

Posterior predictive check is a general concept and practice that can help us understand how well models are capturing different aspects of the data. We can perform posterior predictive checks with just one model or with many models, and thus we can use it as a method for model comparison. Posterior predictive checks are generally done via visualizations, but numerical summaries like Bayesian values can also be helpful.

Good models have a good balance between complexity and predictive accuracy. We exemplified this feature by using the classical example of polynomial regression. We discussed two methods to estimate the out-of-sample accuracy without leaving data aside: cross-validation and information criteria. From a practical point of view, information criteria is a family of theoretical methods looking to balance two...