Posterior predictive checks is a general concept and practice that can help us understand how well models are capturing the data and how well the model is capturing the aspects of a problem we are interested in. 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. We focused our discussion on the latter. From a practical point of view, information criteria is a...