VanVleck (1979 and probably the Green Book) shows that (in our notation) $latex Var(u|\hat{u} )=(1-rel)Var(u) $latex. However, $latex Var(u|\hat{u})$latex is the same as $latex Var(u|y)$latex . So we can put:
$latex 1-rel=\frac{Var(u│y)}{Var(u)} $latex
And thus
$latex rel=1- \frac{Var(u│y)}{Var(u)} = 1- \frac{PEV}{Var(u)} $latex
which is the usual equation. So, reliability is 1 minus the ratio of reduction from prior to posterior variance. It is an inbteresting Bayesian interpretation of which I was not aware.
