[Out sick for a few days; hence no posts.]
Bovy and I spent a lot of today discussing distribution functions, in the context of Rix's (really Reid's) masers and the Solar System. This was partially inspired by Tremaine sending us an alternative method to the inference problem we solved before April Fools' Day. The issue of interest is that of modeling distribution functions when you don't know what model space to use. In Bayesian inference there are ways of giving literally infinite freedom to the distribution function and nonetheless getting a reasonable posterior distribution, fundamentally because the method returns not an answer but a distribution. That said, it is not clear anything in this area is practically relevant. One place it might be is Reid's masers, where the paucity of data makes good inference important, and makes complicated methods tractable.