  The next Galactic core-collapse supernova (SN) should yield a large number of
observed neutrinos. Using Bayesian techniques, we show that with an SN at a
known distance up to 25 kpc, the neutrino events in a water Cherenkov detector
similar to Super-Kamiokande (SK) could be used to distinguish between seven
one-dimensional neutrino emission models assuming no flavor oscillations or the
standard Mikheyev-Smirnov-Wolfenstein effect. Some of these models could still
be differentiated with an SN at a known distance of 50 kpc. We also consider
just the relative distributions of neutrino energy and arrival time predicted
by the models and find that a detector like SK meets the requirement to
distinguish between these distributions with an SN at an unknown distance up to
$\sim 10$ kpc.
