I need a rather a prior on the parameters of a Beta distribution (i.e. $\alpha$ and $\beta$). I have an external constraint that requires me to use univariate priors, one for $\alpha$ and one $\beta$.
Ideally I would like to use two univariate priors that together are as close as possible to something like $p(\alpha,\beta)∝(\alpha+\beta)^{−5/2}$ (for anyone interested in this particular choice, see this thread)
What priors can I use for them?