Star-galaxy classification is one of the most fundamental data-processing
tasks in survey astronomy, and a critical starting point for the scientific
exploitation of survey data. For bright sources this classification can be done
with almost complete reliability, but for the numerous sources close to a
survey's detection limit each image encodes only limited morphological
information. In this regime, from which many of the new scientific discoveries
are likely to come, it is vital to utilise all the available information about
a source, both from multiple measurements and also prior knowledge about the
star and galaxy populations. It is also more useful and realistic to provide
classification probabilities than decisive classifications. All these
desiderata can be met by adopting a Bayesian approach to star-galaxy
classification, and we develop a very general formalism for doing so. An
immediate implication of applying Bayes's theorem to this problem is that it is
formally impossible to combine morphological measurements in different bands
without using colour information as well; however we develop several
approximations that disregard colour information as much as possible. The
resultant scheme is applied to data from the UKIRT Infrared Deep Sky Survey
(UKIDSS), and tested by comparing the results to deep Sloan Digital Sky Survey
(SDSS) Stripe 82 measurements of the same sources. The Bayesian classification
probabilities obtained from the UKIDSS data agree well with the deep SDSS
classifications both overall (a mismatch rate of 0.022, compared to 0.044 for
the UKIDSS pipeline classifier) and close to the UKIDSS detection limit (a
mismatch rate of 0.068 compared to 0.075 for the UKIDSS pipeline classifier).
The Bayesian formalism developed here can be applied to improve the reliability
of any star-galaxy classification schemes based on the measured values of
morphology statistics alone.Comment: Accepted 22 November 2010, 19 pages, 17 figure