At the end of the day yesterday, Price-Whelan and I discussed his very nice project with Kathryn Johnston, in which they
run the clock backwards on stars in stellar streams in the Milky Way and use their clustering properties back in time to identify better and worse gravitational potential models. They are using the empirical variance tensor of a set of 6-displacements (in phase space) as the objective function that they are trying to minimize.
As my loyal readers know, HOGG SMASH objective functions that are not justifiable in terms of probabilistic inference. So today I sketched out a method (in LaTeX) that fits the past-time distribution of stars with a Gaussian (with that pesky variance tensor), plus a bunch of nuisance parameters. That is, I made a likelihood function for their problem. What I have proposed is justifiable and probabilistic—so I am pleased—and it retains the
penalize with the variance aspect that APW and KVJ have been using. I have to admit, however, that inference with my likelihood function will be far, far slower than what they are doing now. It reminds me of our tag line for The Tractor:
It took one hell of a long time, but I felt so probabilistically righteous.