Logarithmic scoring rule
= Logarithmic scoring rule
{title2=$S(p,y)=\log p(y)$}
Under true density $q$, the advantage of truthful reporting is the <Kullback-Leibler divergence> $D_{\rm KL}(q\Vert p)$. Its nonnegativity and equality condition prove strict propriety when the expected log scores are well defined.