Learning about stars and about the Milky Way from imaging and spectroscopy surveys.

This has been a topic going around in my head for quite a while: what can you learn about an individual star (mass, age,distance,metallicity) from spectroscopic, astrometric and photometric observations and what can you learn about the Galaxy from the sum of these observations. That is of course the whole program of huge surveys, including Gaia, and people have worked on it for decades. Usually people deal with age-determinations from high-rez spectra and good parallax distance in the absence of strong reddening or with distance determinations for main-sequence stars with photometric metallicity estimates. [Which may be a wise way to break down the project to something manageable.]

 - for writing a review - I tried to find a good reference or Figure, where people had taken a step back and layer out which aspect of the problem is related to which, and found no good write-up.

Overall, the answer - trivially - is: it depends on the stars themselves, their distances (and extinctions) and of the kinds of data themselves.

Because I could not find a simple graphical representations of: what data do you need to learn what? and what inferences depends on what other pieces of the puzzle? the following plot originated. This has also been part of an exercise to learn how to draw up graphical models myself. I got some tutoring from Dan Foreman-Mackey, who drew up the original version on a blackboard, after my verbal descriptions.

A first attempt at representing inference form stellar MW surveys in a graphical model.
The quantities in the thin dashed circles represent the stellar desiderata (what we want
know about each star), the quantities in the thick dotted circles are the observables that
are typically derived from astrometry, photometry or spectroscopy. The structure at the
top effectively represents priors from our overall picture of the Milky Way. The second
row from the bottom represents stellar astrophysics (isochrone etc..)

Of course, sub-sets of this have been implemented manyfold in the astrophysical literature, and Burnett and Binney have implemented a machinery along the above lines. Their representation is, however, not deemed very intuitive by all attempting readers. I am now having various discussion (Bovy, Schlafly, Hogg, etc..) to see whether it is worth getting serious about this.