fitting spectroscopic systematics and marginalizing out #GaiaDR1

In the morning, I discussed new NYU graduate student Jason Cao's project to generalize The Cannon to fit for radial-velocity offsets and line-spread function variations at test time. This involves generalizing the model, but in a way that doesn't make anything much more computationally complex.

In the afternoon, I had a realization that we probably can compute fully marginalized likelihoods for the wide-separation binary problem in Gaia DR1 TGAS. The idea is that if we treat the velocity distribution as Gaussian, and the proper-motion errors as Gaussian, then at fixed true distance there is an analytic velocity integral. That reduces the marginalization to only two non-analytic dimensions (the true distances to the two stars). I started to work out the math and then foundered on the rocks of completing the square in the case of non-square matrix algebra. No problem really; we have succeeded before (in our K2 work).

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