correcting wrong simulations, linear edition

Soledad Villar (JHU) and I spent some time today constructing (on paper) a model to learn simultaneously from real and simulated data, even when the simulations have large systematic problems. The idea is to model the joint distribution of the real data, the simulated data, and the parameters of the simulated data. Then, using that model, infer the parameters that are most appropriate for each real data point. The problem setup has two modes. In one (which applies to, say, the APOGEE stellar spectra), there is a best-fit simulation for each data example. In the other, there is an observed data set (say, a cosmological large-scale structure survey) and many simulations that are relevant, but don't directly correspond one-to-one. We are hoping we have a plan for either case. One nice thing is: If this works, we will have a model not just for APOGEE stellar parameter estimation, but also for the missing physics in the stellar atmosphere simulations!