Rejected-proposal distribution
= Rejected-proposal distribution
{title2=$r(z)=\frac{Mg(z)-f(z)}{M-1}$}
With normalized densities $f,g$ and envelope $f\leq Mg$, $M>1$, conditioning a proposal on rejection gives density $r=(Mg-f)/(M-1)$. It can be used as an <importance sampling> proposal only if it covers the relevant target support. If $Mg=f$ on a set of positive target mass, rejected draws never visit that set.