Acceptance mass for an unnormalized rejection envelope (source code)

= Acceptance mass for an unnormalized rejection envelope
{title2=$p_{\rm acc}=C/M$}

If $f\geq0$, $C=\int f\in(0,\infty)$ and $f(x)\leq Mg(x)$ for a proposal <probability density function> $g$, accept a proposal $Y$ when an <independent> <uniform distribution> value is at most $f(Y)/(Mg(Y))$. Integrating the joint acceptance <probability density function> gives $p_{\rm acc}=C/M$ and conditional accepted <probability density function> $f/C$. For $n$ <independent> proposals the accepted count has <binomial distribution> with parameters $n,C/M$.