The **Bayesian information criterion** (BIC) or **Schwarz information criterion** (SIC) is a criterion for model selection in a finite set of models. We prefer the model with the lowest BIC. Its general defenition is^{1}

$$ \text{BIC} = \log N\cdot d - 2\ \text{loglik} ,$$

where $N$ is the number of data points $d$ is the number of parameters estimated by the model and $\text{loglik}$ is the log of the maximized likelihood function.

^{1}

Hastie, T., Tibshirani, R., & Friedman, J. H. (2009). *The elements of statistical learning: data mining, inference, and prediction* (2nd ed). Springer.