I reviewed projects with Bovy this afternoon. This conversation renewed my excitement about the discovery Lang and I made this summer: Catalog matching is something close to NP-hard, or perhaps even ill-posed, even in the best of circumstances. That is, it is impossible to create a matched catalog from two catalogs, one coming, say, from GALEX and one from HST without making assumptions that are unjustified (perhaps even demonstrably wrong) and that will affect significantly the output. This is true even when the two catalogs are without imperfections! The only exceptions are cases in which one catalog is considered
ground truth and we desire only probabilistic information from the other catalog, but even here there will be exceedingly ambiguous catalog entries.
We conceived of a solution to this problem, which involves image modeling, where that modeling can be of the original imaging data on which the catalogs were based, or else synthetic imaging created from the catalogs in question. I resolved to write up this solution, with Bovy performing an example analysis to demonstrate its feasability.