what's in an astronomical catalog?

The stars group meeting today wandered into dangerous territory, because it got me on my soap box! The points of discussion were: Are there biases in the Gaia TGAS parallaxes? and How could we use proper motions responsibly to constrain stellar parallaxes? Keith Hawkins (Columbia) is working a bit on the former, and I am thinking of writing something short with Boris Leistedt (NYU) on the latter.

The reason it got me on my soap-box is a huge set of issues about whether catalogs should deliver likelihood or posterior information. My view—and (I think) the view of the Gaia DPAC—is that the TGAS measurements and uncertainties are parameters of a parameterized model of the likelihood function. They are not parameters of a posterior, nor the output of any Bayesian inference. If they were outputs of a Bayesian inference, they could not be used in hierarchical models or other kinds of subsequent inferences without a factoring out of the Gaia-team prior.

This view (and this issue) has implications for what we are doing with our (Liestedt, Hawkins, Anderson) models of the color–magnitude diagram. If we output posterior information, we have to also output prior information for our stuff to be used by normals, down-stream. Even with such output, the results are hard to use correctly. We have various papers, but they are hard to read!

One comment is that, if the Gaia TGAS contains likelihood information, then the right way to consider its possible biases or systematic errors is to build a better model of the likelihood function, given their outputs. That is, the systematics should be created to be adjustments to the likelihood function, not posterior outputs, if at all possible.

Another comment is that negative parallaxes make sense for a likelihood function, but not (really) for a posterior pdf. Usually a sensible prior will rule out negative parallaxes! But a sensible likelihood function will permit them. The fact that the Gaia catalogs will have negative parallaxes is related to the fact that it is better to give likelihood information. This all has huge implications for people (like me, like Portillo at Harvard, like Lang at Toronto) who are thinking about making probabilistic catalogs. It's a big, subtle, and complex deal.


  1. Just to be pedantic... I also recall DWH saying "there is always a prior. Sometimes hard to write down.".

    More seriously, TGAS gives posterior values using even inconsistent prior functions. Gaia DR2 will make those self-consistent. Do you mean in this context prior = things we'd never want to change?

    1. The fact that one always has prior beliefs does not mean that one has to report the posterior pdf as output. I am sorry if it is true that TGAS is reporting posterior rather than likelihood information! I think with the setup in Michalik's paper, you could report either.