p(z)

At group meeting, Malz discussed this paper by Sheldon et al, which obtains a redshift distribution and individual-object photometric redshifts from photometric data and a heterogeneous training set of objects with spectroscopic redshifts. The Sheldon paper (which refers to the Cunha method) is an example of a likelihood-free inference, in that it creates a redshift distribution and posteriors for redshift for individual objects without ever giving a likelihood function. This is good, in a way, because it doesn't require parameterizing galaxy spectral energy distributions. But it is bad, because, for one, any user of these probabilistic outputs wants likelihood information not posterior information! And more bad because we do have ideas about the probability of the data—we know things about the noise in photometric space—that are the principal inputs to a likelihood function. Malz and I plan to write some kind of paper about all this, but we are still confused about exactly what that paper would contain.