information theory and phase space

At Groningen (my first stop on my trip), I chatted with Robyn Sanderson (Groningen) about finding substructure in current SDSS-II and future Gaia stellar kinematic data. The idea we quickly worked out—which maybe is in the literature already—is to ask a general information-theory-like question about the phase-space distribution function in something like action space, and then tune potential parameters to make the answer to that question as informative as possible. As a straw man idea, I suggested the K–L divergence between the action distribution and a maximum entropy distribution with the same low-order moments. The thing I like about this plan is that it might not be very sensitive to the observational noise. That is, the scalar will be sensitive to it, but the optimum in parameter space might not. I said might. It's worth a try.