I have spent part of the summer working with Megan Bedell (Chicago) to see if there is any evidence that radial velocity measurements with the HARPS instrument might be being affected by calibration issues or helped by taking some kind of hierarchical approach to calibration. We weren't building that hierarchical model, we were looking to see if there is evidence in the residuals for information that a hierarchical model could latch on to. We found nothing, to my surprise. I think this means that the HARPS pipelines are absolutely awesome. I think they are closed-source, so we can't do much but inspect the output.
Given this, we decided to start looking at stellar diagnostics—if it isn't the instrument calibration, then maybe it is actually the star itself: We need to ask whether we can we see spectral signatures that predict radial velocity. This is a very general causal formulation of the problem: We do not expect that a star's spectrum will vary with the phase of an exoplanet's orbit (unless it is a very hot planet!), so if anything about the spectrum predicts the radial velocity, we have something to latch on to. The idea is that we might see the spectral signature of hot up-welling or cold down-welling at the stellar surface. There is much work in this area, but I am not sure than anyone has done anything truly data driven (in the style, for example, of The Cannon). We discussed first steps towards doing that, with Bedell assigned plotting tasks, and me writing down some methodological ideas.Over lunch, Boris Leistedt and I caught up on all the various projects we like to discuss. He has had the breakthrough that—if you build a proper generative model for galaxy imaging data—you don't need to have spectroscopic training sets, nor good galaxy spectral models, to get good photometric redshifts. The idea is that once you have multi-band photometry, you can predict the appearance of any observed galaxy as it would appear any other redshift using a flexible, non-parametric SED model that isn't tied to any physical galaxy model. The idea is that we use all of, but only, what we believe about how the redshift works, physically. Most machine-learning methods aren't required to get the redshift physics right, and most template-based models assume lots of auxilliary things about stars and stellar populations and dust. We also realized that, if done correctly, this method could subsume into itself the cross-correlation redshifts that the LSST project is excited about.