The candidate models correspond to a restrictive class of mechanism and the comparison of the candidate models is based on comparison of fit scores at fixed complexity. The fit score used for comparison is the likelihood score derived by Hyvärinen and Smith in this case as: $S_{X\rightarrow Y} = -[\sum_{i=1}^n G_X(x^i)+G_{N_Y}(\frac{y^i - \rho x^i}{\sqrt{1-\rho^2}})]+n\log (1-\rho^2)$ where $G_X ( u ) = \log P_X ( u )$ and $G_{N_Y}$ is the standardized log probability distribution function of the residual when regressing Y on X . $S_{Y → X}$ is computed similarly and the causal direction is decided by comparing $S_{X → Y}$ with $S_{Y → X}$.