Bayesian Inference of Globular Cluster Properties Using Distribution
  Functions
  We present a Bayesian inference approach to estimating the cumulative mass
profile and mean squared velocity profile of a globular cluster given the
spatial and kinematic information of its stars. Mock globular clusters with a
range of sizes and concentrations are generated from lowered isothermal
dynamical models, from which we test the reliability of the Bayesian method to
estimate model parameters through repeated statistical simulation. We find that
given unbiased star samples, we are able to reconstruct the cluster parameters
used to generate the mock cluster and the cluster's cumulative mass and mean
velocity squared profiles with good accuracy. We further explore how strongly
biased sampling, which could be the result of observing constraints, may affect
this approach. Our tests indicate that if we instead have biased samples, then
our estimates can be off in certain ways that are dependent on cluster
morphology. Overall, our findings motivate obtaining samples of stars that are
as unbiased as possible. This may be achieved by combining information from
multiple telescopes (e.g., Hubble and Gaia), but will require careful modeling
of the measurement uncertainties through a hierarchical model, which we plan to
pursue in future work.
