Determining the velocity dispersion of the thick disc
  We attempt to recover the mean vertical velocity and vertical velocity
dispersion as a function of the Galactic height for a sample drawn from a
realistic Galaxy distribution function by following the method presented in
Moni Bidin et al. (2012). We find that, for the sample size used, the
observational error in the velocities is much smaller than the Poisson noise
which has not been accounted for by Moni Bidin et al. We repeat the analysis on
a large number of samples to estimate the contribution of the Poisson noise and
to uncover any systematics. We find that the dispersion is systematically
overestimated at low Galactic heights and slightly underestimated at high
Galactic heights leading to an underestimate of the gradient of the dispersion
with Galactic height. The causes of the systematics are revealed by repeating
the calculation using a method inspired by Girard et al. (2006). This method
recovers the expected dispersion much more successfully and in particular
yields a gradient of the dispersion with Galactic height which is approximately
three times that found using the method presented by Moni Bidin et al.
