Bayes versus the virial theorem: inferring the potential of a galaxy
  from a kinematical snapshot
  We present a new framework for estimating a galaxy's gravitational potential,
Phi(x), from its stellar kinematics by adopting a fully non-parametric model
for the galaxy's unknown action-space distribution function, f(J). Having an
expression for the joint likelihood of Phi and f, the likelihood of Phi is
calculated by using a Dirichlet process mixture to represent the prior on f and
marginalising. We demonstrate that modelling machinery constructed using this
framework is successful at recovering the potentials of some simple systems
from perfect discrete kinematical data, a situation handled effortlessly by
traditional moment-based methods, such as the virial theorem, but in which
other, more modern, methods are less than satisfactory. We show how to
generalise the machinery to account for realistic observational errors and
selection functions. A practical implementation is likely to raise some
interesting algorithmic and computational challenges.
