Bovy and I discussed two of his dynamical inference problems today. The first is with Reid's masers, where Bovy finds, when he marginalizes over even the most basic unknowns, that the masers are not highly informative about the potential (or rotation curve) of the Milky Way. That is not to say that we don't have much knowledge about the potential, but just that the masers aren't the source of it. We differ from Reid et al in our conclusions because we aren't as confident about the input assumptions.
The second is the Solar System demo paper. Tremaine proposed some methods that treat the eccentricity distribution better and don't depend on the energy distribution. We are not sure that there is any way to write the problem down that is insensitive to the energy distribution that doesn't make other assumptions we are unhappy about. This all gets at the question of how
generative your generative model needs to be. Does it really need to generate your observations? And if so, at what level? I think ideally at whatever level your observational uncertainties are simple (understood, uncorrelated, close to Gaussian, and so on).