  We consider the statistical problem of catalogue matching from a machine
learning perspective with the goal of producing probabilistic outputs, and
using all available information. A framework is provided that unifies two
existing approaches to producing probabilistic outputs in the literature, one
based on combining distribution estimates and the other based on combining
probabilistic classifiers. We apply both of these to the problem of matching
the HIPASS radio catalogue with large positional uncertainties to the much
denser SuperCOSMOS catalogue with much smaller positional uncertainties. We
demonstrate the utility of probabilistic outputs by a controllable completeness
and efficiency trade-off and by identifying objects that have high probability
of being rare. Finally, possible biasing effects in the output of these
classifiers are also highlighted and discussed.
