In my view, the introduction of a paper should contextualize, bring up, form, and ask questions, and the discussion section at the end should answer them, or fail to, or answer them with caveats. The discussion should say all the respects in which the answers given are or could be or shoud be wrong. We only understand things by understand what they don't do. (And no paper should have a "summary" section: Isn't that the abstract?) Ness and I assembled our conclusions, caveats, and questions about The Cannon into an outline for the discussion section. We also talked a bit more about figures. She spent the day working on discussion and I worked a bit on the abstract.
In group meeting, we looked at Malz's first models of SDSS sky. Foreman-Mackey brought up the deep question: If we have a flexible model for the sky in SDSS fibers, how can we fit or constrain it without fitting out or distorting the true spectra of the astronomical objects that share the fibers? Great question, and completely analogous to the problem being solved by Wang in our model for Kepler pixels: How do we separate the signals caused by the spacecraft from those caused by exoplanets?
We are approaching Wang's problem by capitalizing on the causal or conditional independence properties of our generative model. But this is imperfect, since there are hyper-priors and hyper-hyper-priors that make everything causally related to everything else, in some sense. One example in the case of sky: Atomic and molecular physics in the atmosphere is the same atomic and molecular physics acting in stellar atmospheres and the interstellar medium in the spectra of astronomical sources. Another example: The line-spread function in the spectrograph is the same for sky lines and for galaxy emission and absorption lines. These kinds of commonalities make the "statistically independent" components in fact very similar.
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