We present a general probabilistic formalism for cross-identifying
astronomical point sources in multiple observations. Our Bayesian approach,
symmetric in all observations, is the foundation of a unified framework for
object matching, where not only spatial information, but physical properties,
such as colors, redshift and luminosity, can also be considered in a natural
way. We provide a practical recipe to implement an efficient recursive
algorithm to evaluate the Bayes factor over a set of catalogs with known
circular errors in positions. This new methodology is crucial for studies
leveraging the synergy of today's multi-wavelength observations and to enter
the time-domain science of the upcoming survey telescopes.Comment: Accepted for publication in the Astrophysical Journal, 8 pages, 1
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