Reliability of the measured velocity anisotropy of the Milky Way stellar halo
  Determining the velocity distribution of halo stars is essential for
estimating the mass of the Milky Way and for inferring its formation history.
Since the stellar halo is a dynamically hot system, the velocity distribution
of halo stars is well described by the 3-dimensional velocity dispersions
$(\sigma_r, \sigma_\theta, \sigma_\phi)$, or by the velocity anisotropy
parameter $\beta=1-(\sigma_\theta^2+\sigma_\phi^2)/(2\sigma_r^2)$. Direct
measurements of $(\sigma_r, \sigma_\theta, \sigma_\phi)$ consistently suggest
$\beta =0.5$-$0.7$ for nearby halo stars. In contrast, the value of $\beta$ at
large Galactocentric radius $r$ is still controversial, since reliable proper
motion data are available for only a handful of stars. In the last decade,
several authors have tried to estimate $\beta$ for distant halo stars by
fitting the observed line-of-sight velocities at each radius with simple
velocity distribution models (local fitting methods). Some results of local
fitting methods imply $\beta<0$ at $r \gtrsim 20 \;\rm{kpc}$, which is
inconsistent with recent predictions from cosmological simulations. Here we
perform mock-catalogue analyses to show that the estimates of $\beta$ based on
local fitting methods are reliable only at $r \leq 15 \;\rm{kpc}$ with the
current sample size ($\sim10^3$ stars at a given radius). As $r$ increases, the
line-of-sight velocity (corrected for the Solar reflex motion) becomes
increasingly closer to the Galactocentric radial velocity, so that it becomes
increasingly more difficult to estimate tangential velocity dispersion
$(\sigma_\theta, \sigma_\phi)$ from line-of-sight velocity distribution. Our
results suggest that the forthcoming Gaia data will be crucial for
understanding the velocity distribution of halo stars at $r \geq 20\;\rm{kpc}$.
