Those kind of methods reason at fixed complexity $C_{\hat{\mathcal{B}}}(\theta)$ and choose the causal direction according to the best fit. 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 $S_{\hat{\mathcal{B}}}(\theta)$ and for the purposes of simplified notations, we note $S_{X\rightarrow Y}(\hat{\theta})$ the best fit score corresponding to the model $\mathcal{B}_{\hat{\mathcal{G}}, \hat{f}, Q_N}$ with $\hat{\mathcal{G}} = X\rightarrow Y$.

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