I would like to create a "weakly informative" prior distribution for a couple parameters. They both could theoretically take any value between 0 and 1, but I have reason to think that they should be negatively correlated. Is there any sort of standard joint distribution (a beta-analogue to the multivariate normal?) where I could easily specify such a distribution?
In looking around, I've read about the Dirichlet distribution, which seems to be almost perfect, but inappropriate because of it's requirement that the sum = 1.