The cross-identification of sources in separate catalogs is one of the most
basic tasks in observational astronomy. It is, however, surprisingly difficult
and generally ill-defined. Recently Budav\'ari & Szalay (2008) formulated the
problem in the realm of probability theory, and laid down the statistical
foundations of an extensible methodology. In this paper, we apply their
Bayesian approach to stars that, we know, can move measurably on the sky, with
detectable proper motion, and show how to associate their observations. We
study models on a sample of stars in the Sloan Digital Sky Survey, which allow
for an unknown proper motion per object, and demonstrate the improvements over
the analytic static model. Our models and conclusions are directly applicable
to upcoming surveys such as PanSTARRS, the Dark Energy Survey, Sky Mapper, and
the LSST, whose data sets will contain hundreds of millions of stars observed
multiple times over several years.Comment: 10 pages, 5 figure
