  A powerful method to measure the mass profile of a galaxy is through the
velocities of tracer particles distributed through its halo. Transforming this
kind of data accurately to a mass profile M(r), however, is not a trivial
problem. In particular, limited or incomplete data may substantially affect the
analysis. In this paper we develop a Bayesian method to deal with incomplete
data effectively; we have a hybrid-Gibbs sampler that treats the unknown
velocity components of tracers as parameters in the model. We explore the
effectiveness of our model using simulated data, and then apply our method to
the Milky Way using velocity and position data from globular clusters and dwarf
galaxies. We find that in general, missing velocity components have little
effect on the total mass estimate. However, the results are quite sensitive to
the outer globular cluster Pal 3. Using a basic Hernquist model with an
isotropic velocity dispersion, we obtain credible regions for the cumulative
mass profile M(r) of the Milky Way, and provide estimates for the model
parameters with 95 percent Bayesian credible intervals. The mass contained
within 260 kpc is 1.37x10^12 solar masses, with a 95 percent credible interval
of (1.27,1.51)x10^12 solar masses. The Hernquist parameters for the total mass
and scale radius are 1.55 (+0.18/-0.13)x10^12 solar masses and 16.9 (+4.8/-4.1)
kpc, where the uncertainties span the 95 percent credible intervals. The code
we developed for this work, Galactic Mass Estimator (GME), will be available as
an open source package in the R Project for Statistical Computing.
