My flight home got seriously delayed and I had an extra day in Aspen. I spent it talking about (and working on) my project to infer dynamical invariants in the well-mixed parts of the Milky Way from chemical (element-abundance) invariants. I had various epiphanies and useful discussions:
Rix (MPIA) and I worked on how you explain the project to the world. One explanation is this: In addition to dynamical invariants, there are chemical abundances, which depend on the dynamical invariants (and not on the conjugate angles). Therefore inference of the dynamical invariants must be better or improved if you model the abundance invariants as well or in tandem. Another explanation is this: Imagine you do a dynamical inference (like Jeans modeling) and you (effectively) determine orbit structure. If you are slightly off, the element abundances you have measured will reveal the issues, and can be used to adjust or update or improve the orbit-structure inference, because stars don't change their abundances as they orbit!
Price-Whelan (Princeton) and I worked on how to compare the project with Jeans modeling, Schwarzschild modeling, or fully marginalized forward modeling of the kinematics (which has almost never been done). I have a scaling argument that my new method must be better than any of these: Each of these methods gets some amount of information out of the positions and velocities of the stars. My chemical-tangents method gets more information from every new element abundance you measure (even if each new element is fully covariant physically with the ones you have measured before; it is the measurements that are near-independent). So in some limit (and I think that limit arrives very early), it will have more information than any of these methods. But of course I need to demonstrate this quantitatively in the very near future.
Another point of comparison is related to the conditional or generative or causal structure of the model: I am modeling the abundance distribution conditioned on the phase-space positions. This means that I don't need to know the selection function of the survey, which Jeans modeling does (to some extent) and the more serious methods do (to great precision). On the other hand, because I am conditioning on the positions and not generating them, I can't (gracefully) account for measurement uncertainties in position. (Of course that's true for Jeans too.)
Anyway, the reason I am writing all this is because: The best practice for writing (the paper) is writing (this blog and emails and etc).
No comments:
Post a Comment