must face degeneracies

In my project to match GALEX and SDSS sources, I am modeling the distribution of all close coincidences (on the sky) between GALEX and SDSS catalog entries as a sum of two distributions, one for false matches and one for true matches. These two distributions are differently constrained; for example in the false match distribution the GALEX and SDSS properties should be separable, and the angular distribution should be consistent with little or no clustering.

Unfortunately, as I mentioned a few days ago, the true match distribution has the freedom, in what I am currently doing, to mimic the false distribution (though the false match distribution does not have the freedom to mimic the true distribution). I experimented with hacky ways to deal with this today, and decided that I must figure out and take a principled approach.