On evaluating models, either in-sample or out-of-sample.
In-sample model evaluation techniques can be based on measures of fit or loss-functions, but note that in-sample fit will typically increase spuriously as the model becomes more complex, which is called overfitting. For this reason, typically in-sample fit is penalized based on model complexity, like adjusted r-squared, aic or bic. AIC and BIC are also examples of information criteria, which can also be used in-sample.
Out-of-sample model evaluation usually relies on predictive accuracy and again on loss-functions. Distributional predictions can be evaluated using scoring-rules.
