  We introduce a new methodology to robustly determine the mass profile, as
well as the overall distribution, of Local Group satellite galaxies.
Specifically we employ a statistical multilevel modelling technique, Bayesian
hierarchical modelling, to simultaneously constrain the properties of
individual Local Group Milky Way satellite galaxies and the characteristics of
the Milky Way satellite population. We show that this methodology reduces the
uncertainty in individual dwarf galaxy mass measurements up to a factor of a
few for the faintest galaxies. We find that the distribution of Milky Way
satellites inferred by this analysis, with the exception of the apparent lack
of high-mass haloes, is consistent with the Lambda cold dark matter
(Lambda-CDM) paradigm. In particular we find that both the measured
relationship between the maximum circular velocity and the radius at this
velocity, as well as the inferred relationship between the mass within 300 pc
and luminosity, match the values predicted by Lambda-CDM simulations for halos
with maximum circular velocities below 20 km/sec. Perhaps more striking is that
this analysis seems to suggest a more cusped "average" halo shape that is
shared by these galaxies. While this study reconciles many of the observed
properties of the Milky Way satellite distribution with that of Lambda-CDM
simulations, we find that there is still a deficit of satellites with maximum
circular velocities of 20-40 km/sec.
