Probabilistic record linkage in astronomy: Directional
  cross-identification and beyond
  Modern astronomy increasingly relies upon systematic surveys, whose dedicated
telescopes continuously observe the sky across varied wavelength ranges of the
electromagnetic spectrum; some surveys also observe non-electromagnetic
"messengers," such as high-energy particles or gravitational waves. Stars and
galaxies look different through the eyes of different instruments, and their
independent measurements have to be carefully combined to provide a complete,
sound picture of the multicolor and eventful universe. The association of an
object's independent detections is, however, a difficult problem
scientifically, computationally, and statistically, raising varied challenges
across diverse astronomical applications. The fundamental problem is finding
records in survey databases with directions that match to within the direction
uncertainties. Such astronomical versions of the record linkage problem are
known by various terms in astronomy: cross-matching, cross-identification, and
directional, positional, or spatio-temporal coincidence assessment. Astronomers
have developed several statistical approaches for such problems, largely
independently of related developments in other disciplines. Here we review
emerging approaches that compute (Bayesian) probabilities for the hypotheses of
interest: possible associations, or demographic properties of a cosmic
population that depend on identifying associations. Many cross-identification
tasks can be formulated within a hierarchical Bayesian partition model
framework, with components that explicitly account for astrophysical effects
(e.g., source brightness vs. wavelength, source motion, or source extent),
selection effects, and measurement error. We survey recent developments, and
highlight important open areas for future research.
