why make a dust map? and Bayesian model elaboration

Lauren Anderson (Carnegie) and I had a wide-ranging conversation today. But part of it was about the dust map: We have a project with statisticians to deliver a three-dimensional dust map, using a very large Gaussian-process model. Right now the interesting parts of the project are around model checking and model elaboration: How do you take a model and decide what's wrong with it, in detail. Meaning: Not compare it to other models (that's a solved problem, in principle), but rather, compare it to the data and see where it would benefit from improvement.

One key idea for model elaboration is to check the parts of the model you care about and see if those aspects are working well. David Blei (Columbia) told us to climb a mountain and think on this matter, so we did, today. We decided that our most important goals are (1) to deliver accurate extinction values to stellar targets, for our users, and (2) to find interesting dust structures (like spiral arms) if they are there in the data.

Now the challenge is to convert these considerations into posterior predictive checks that are informative about model assumptions. The challenge is that, in a real-data Bayesian inference, you don't know the truth! You just have your data and your model.