a prior on the CMD isn't a prior on distance, exactly

Today my research time was spent writing in the paper by Lauren Anderson (Flatiron) about the TGAS color–magnitude diagram. I think of it as being a probabilistic inference in which we put a prior on stellar distances and then infer the distance. But that isn't correct! It is an inference in which we put a prior on the color–magnitude diagram, and then, given noisy color and (apparent) magnitude information, this turns into an (effective, implicit) prior on distance. This Duh! moment led to some changes to the method section!