Gaussian log-rate correction to the Poisson trick
= Gaussian log-rate correction to the Poisson trick
{c}
{title2=$R(S)=\mathbb E_{\Gamma(n,1)}e^{-(\log V-\log S)^2/(2s^2)}$}
A mean-zero <normal distribution> prior of variance $s^2$ on the log baseline multiplies the multinomial kernel by the displayed correction, up to a constant independent of coefficients. The factor is not constant in $S$, so the posterior equivalence is approximate. <Dominated convergence> makes it tend to one as $s^2$ tends to infinity.