  We investigate a novel Bayesian analysis method, based on the Stochastically
Lighting Up Galaxies (slug) code, to derive the masses, ages, and extinctions
of star clusters from integrated light photometry. Unlike many analysis
methods, slug correctly accounts for incomplete IMF sampling, and returns full
posterior probability distributions rather than simply probability maxima. We
apply our technique to 621 visually-confirmed clusters in two nearby galaxies,
NGC 628 and NGC 7793, that are part of the Legacy Extragalactic UV Survey
(LEGUS). LEGUS provides Hubble Space Telescope photometry in the NUV, U, B, V,
and I bands. We analyze the sensitivity of the derived cluster properties to
choices of prior probability distribution, evolutionary tracks, IMF,
metallicity, treatment of nebular emission, and extinction curve. We find that
slug's results for individual clusters are insensitive to most of these
choices, but that the posterior probability distributions we derive are often
quite broad, and sometimes multi-peaked and quite sensitive to the choice of
priors. In contrast, the properties of the cluster population as a whole are
relatively robust against all of these choices. We also compare our results
from slug to those derived with a conventional non-stochastic fitting code,
Yggdrasil. We show that slug's stochastic models are generally a better fit to
the observations than the deterministic ones used by Yggdrasil. However, the
overall properties of the cluster populations recovered by both codes are
qualitatively similar.
