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Modern astronomy increasingly relies upon systematic surveys, whose dedicatedtelescopes continuously observe the sky across varied wavelength ranges of theelectromagnetic spectrum; some surveys also observe non-electromagnetic"messengers," such as high-energy particles or gravitational waves. Stars andgalaxies look different through the eyes of different instruments, and theirindependent measurements have to be carefully combined to provide a complete,sound picture of the multicolor and eventful universe. The association of anobject's independent detections is, however, a difficult problemscientifically, computationally, and statistically, raising varied challengesacross diverse astronomical applications. The fundamental problem is findingrecords in survey databases with directions that match to within the directionuncertainties. Such astronomical versions of the record linkage problem areknown by various terms in astronomy: cross-matching, cross-identification, anddirectional, positional, or spatio-temporal coincidence assessment. Astronomershave developed several statistical approaches for such problems, largelyindependently of related developments in other disciplines. Here we reviewemerging approaches that compute (Bayesian) probabilities for the hypotheses ofinterest: possible associations, or demographic properties of a cosmicpopulation that depend on identifying associations. Many cross-identificationtasks can be formulated within a hierarchical Bayesian partition modelframework, 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, andhighlight important open areas for future research.

Probabilistic record linkage in astronomy: Directional cross-identification and beyond