Best complexity methods for determining causal direction assume a comparative fit $P = Q$ in both directions and choose the causal direction by comparing the complexity terms. 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 $C_{\hat{\mathcal{B}}}(\theta)$. Let $C_{X\rightarrow Y}(\hat{\theta})$ be 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 rightarrow Y, otherwise it is decided that Y rightarrow X.