Figure 1

Theoretical AUC as a function of \(\beta\) assuming \(g_i\) is Gaussian distributed with mean \(\mu _g\) and standard deviation \(\sigma _g\). Different colors correspond to different values of \(\mu _g\), while line types identify values of \(\sigma _g\). We see that increasing \(\beta\) has the effect of reducing the uncertainty on the random variable \(s_i(t)\), keeping \(g_i\) unchanged. Grey dashed lines at \(\textrm{AUC}=0.5\) and \(\textrm{AUC}=1\) are guides to the eye.