a likelihood function for element abundances

On the flight back to NYC, I worked on building a likelihood function for the dependence of element abundances on dynamical actions. It is a hard problem; what freedom to give the model? I was doing crazy binning experiments, trying to make the model fully non-parametric, but it has annoying pathologies, like that the assignments of stars to bins is strongly dynamical-parameter-dependent. And thus you get a jagged likelihood function. At the end of a long set of numerical experiments on my laptop, I realized the following simple thing (duh):

All the abundance-ratio dependences on vertical action are extremely smooth! So using a parameterized rather than non-parametric form should be absolutely fine. By the time I had this realization, I was done all I could do for the day, so: Tomorrow!