What does the Schwarz Bayesian Criterion (SBC) / likelihood evaluate?

The Schwarz Bayesian Criterion (SBC), often referred to as the Bayesian Information Criterion (BIC), is primarily used for model selection among a finite set of models. It evaluates how well a model fits the data while penalizing for the complexity of the model, which is essential to prevent overfitting.

The SBC combines the likelihood of the model with a penalty term based on the number of parameters in the model and the number of observations. By evaluating this criterion, one can assess the trade-off between the goodness of fit (measured by the likelihood) and model complexity (based on the number of parameters). A lower SBC value suggests a better model when comparing different models.

This criterion does not specifically focus on the difference between prediction estimates and observed values, nor does it strictly measure predictive consistency or overall model performance in an isolated manner. Instead, it provides a systematic approach to select models by balancing fit and complexity. Hence, it is essential in guiding model selection in a principled way rather than just calculating error metrics.