Those methods assume a comparative fit P = Q in both directions and choose the causal direction by comparing the complexity terms. In this case, for any candidate model $\mathcal{B}_{\hat{\mathcal{G}}, \hat{f}, Q_N}$, we note $\hat{\theta}$ the set of parameters that minimizes the score $C_{\hat{\mathcal{B}}}(\theta)$ and $C_{X\rightarrow Y}(\hat{\theta})$ the lowest complexity score corresponding to the model $\mathcal{B}_{\hat{\mathcal{G}}, \hat{f}, Q_N}$ with $\hat{\mathcal{G}} = X\rightarrow Y$.

If $C_{X\rightarrow Y}(\hat{\theta}) < C_{Y\rightarrow X}(\hat{\theta})$ , it is decided that X → Y , otherwise it is decided that Y → X .