Model selection criteria like BIC and AIC are commonly used to pick the best model from a group. However, when dealing with complex systems, these criteria can struggle if variables are closely related or have measurement uncertainties. This study introduces improved versions of these criteria that consider these issues. By using a more advanced approach, the new criteria can better identify relationships between variables even with significant noise present. Simulations using synthetic data show that the upgraded criteria outperform the traditional ones in most cases.