The BIC is a criterion for model selection among a finite set of models; it is based on the likelihood function and incorporates a penalty for the number of parameters in the model. Mathematically, it is expressed as:
\[ \text{BIC} = -2 \ln(L) + k \ln(n) \]
where: - \( L \) is the likelihood of the model, - \( k \) is the number of parameters, - \( n \) is the number of observations.