Best fit methods for determining causal direction reason at a fixed complexity $C_{\hat{\mathcal{B}}}(\theta)$ and choose the causal direction according to the best fit. For any candidate model $\mathcal{B}_{\hat{\mathcal{G}}, \hat{f}, Q_N}$, let $\hat{\theta}$ be the set of parameters that minimizes the score $S_{\hat{\mathcal{B}}}(\theta)$. For simplified notation, let $S_{X\rightarrow Y}(\hat{\theta})$ be 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 rightarrow Y, otherwise it is decided that Y rightarrow X.