= Log-gamma prior for a Poisson log-intercept
{title2=$p(\mu)=b^a\exp(a\mu-be^\mu)/\Gamma(a)$}
If the positive baseline rate has a <gamma distribution> of shape $a$ and rate $b$, its <logarithm> has this <probability density function> with respect to $d\mu$. The extra factor $e^\mu$ is the <Jacobian determinant> of the transformation. After a <Gibbs sampler> draws the conditional baseline rate, taking its <logarithm> is an exact update of the intercept. Omitting the Jacobian changes the prior.
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