Prior distribution on/of a parameter Is it correct to write the prior distribution on $\mu$ ?
I think it is correct because it refers to the fact that "we put a distribution on (the state space of) $\mu$".
However, I would not say the posterior distribution on $\mu$.
This is how I feel it but my feeling is based on the French translation. Is it correct in English ?
 A: Being that the first two results of a Google search (in English) for "prior distribution on" yield papers by Andrew Gelman, I'm sufficiently convinced that "on" is common enough not to cause confusion. Actually, there are contexts in which using "of" would strike some native English speakers as odd. For instance, the phrase "a uniform prior of $log(\sigma$)"—rather than "on $log(\sigma)$," as it reads in one of the Gelman papers—sounds a bit off to my ear. More, "posterior on" is used commonly throughout
So, whether a matter of technical definition or simple convention, it's acceptable. My own bias is to use "on" more frequently than "of," and in some cases I've even seen "for."
A: Why do you want to use on instead of of?
I think that of is more correct because it refers to the fact that we are talking about the distribution of $\mu$ before (prior -> pre -> before) --- the observation of data.
Similarly, I think it is correct "posterior distribution of $\mu$", because it refers to the distribution of $\mu$ after (posterior -> post -> after) we have observed data.
