Resolving the mass--anisotropy degeneracy of the spherically symmetric
  Jeans equation II: optimum smoothing and model validation
  The spherical Jeans equation is widely used to estimate the mass content of a
stellar systems with apparent spherical symmetry. However, this method suffers
from a degeneracy between the assumed mass density and the kinematic anisotropy
profile, $\beta(r)$. In a previous work, we laid the theoretical foundations
for an algorithm that combines smoothing B-splines with equations from dynamics
to remove this degeneracy. Specifically, our method reconstructs a unique
kinematic profile of $\sigma_{rr}^2$ and $\sigma_{tt}^2$ for an assumed free
functional form of the potential and mass density $(\Phi,\rho)$ and given a set
of observed line-of-sight velocity dispersion measurements, $\sigma_{los}^2$.
In Paper I (submitted to MNRAS: MN-14-0101-MJ) we demonstrated the efficiency
of our algorithm with a very simple example and we commented on the need for
optimum smoothing of the B-spline representation; this is in order to avoid
unphysical variational behaviour when we have large uncertainty in our data. In
the current contribution we present a process of finding the optimum smoothing
for a given data set by using information of the behaviour from known ideal
theoretical models. Markov Chain Monte Carlo methods are used to explore the
degeneracy in the dynamical modelling process. We validate our model through
applications to synthetic data for systems with constant or variable
mass-to-light ratio $\Upsilon$. In all cases we recover excellent fits of
theoretical functions to observables and unique solutions. Our algorithm is a
robust method for the removal of the mass-anisotropy degeneracy of the
spherically symmetric Jeans equation for an assumed functional form of the mass
density.
