In 'Bayesian Data Analysis' (Gelman, Carlin, Stern and Rubin) on page 64 it reads:
"If the density of $y$ is such that $p(y-\theta|\theta)$ is a function that is free of $\theta$ and $y$, say $f(u)$ where $u = y - \theta$, then $y - \theta$ is a pivotal quantity, and $\theta$ is called a pure location parameter. In such a case, it is reasonable that a noninformative prior distribution for $\theta$ would give $f(y - \theta)$ for the posterior ditsribution, $p(y - \theta|y)$. That is, under the posterior distribution, $y-\theta$ should still be a pivotal quantity, whose distribution is free of both $\theta$ and $y$. Under this condition, using Bayes' rule, $p(y - \theta|y) \propto p(\theta)p(y - \theta|\theta)$..."
Maybe I'm being dense, but shouldn't Bayes' rule say something like $p(y - \theta|y) \propto p(y - \theta)p(y|y-\theta)$? What am I forgetting to remember here?