  This paper is an invited commentary on Tamas Budavari's presentation, "On
statistical cross-identification in astronomy," for the Statistical Challenges
in Modern Astronomy V conference held at Pennsylvania State University in June
2011. I begin with a brief review of previous work on probabilistic (Bayesian)
assessment of directional and spatio-temporal coincidences in astronomy (e.g.,
cross-matching or cross-identification of objects across multiple catalogs).
Then I discuss an open issue in the recent innovative work of Budavari and his
colleagues on large-scale probabilistic cross-identification: how to assign
prior probabilities that play an important role in the analysis. With a simple
toy problem, I show how Bayesian multilevel modeling (hierarchical Bayes)
provides a principled framework that justifies and generalizes pragmatic rules
of thumb that have been successfully used by Budavari's team to assign priors.
