  We present a hierarchical Bayesian inference approach to estimating the
structural properties and the phase space center of a globular cluster (GC)
given the spatial and kinematic information of its stars based on lowered
isothermal cluster models. As a first step towards more realistic modelling of
GCs, we built a differentiable, accurate emulator of the lowered isothermal
distribution function using interpolation. The reliable gradient information
provided by the emulator allows the use of Hamiltonian Monte Carlo methods to
sample large Bayesian models with hundreds of parameters, thereby enabling
inference on hierarchical models. We explore the use of hierarchical Bayesian
modelling to address several issues encountered in observations of GC including
an unknown GC center, incomplete data, and measurement errors. Our approach not
only avoids the common technique of radial binning but also incorporates the
aforementioned uncertainties in a robust and statistically consistent way.
Through demonstrating the reliability of our hierarchical Bayesian model on
simulations, our work lays out the foundation for more realistic and complex
modelling of real GC data.
