  We report new constraints on the local escape speed of our Galaxy. Our
analysis is based on a sample of high velocity stars from the RAVE survey and
two previously published datasets. We use cosmological simulations of disk
galaxy formation to motivate our assumptions on the shape of the velocity
distribution, allowing for a significantly more precise measurement of the
escape velocity compared to previous studies. We find that the escape velocity
lies within the range $498\kms < \ve < 608 \kms$ (90 per cent confidence), with
a median likelihood of $544\kms$. The fact that $\ve^2$ is significantly
greater than $2\vc^2$ (where $\vc=220\kms$ is the local circular velocity)
implies that there must be a significant amount of mass exterior to the Solar
circle, i.e. this convincingly demonstrates the presence of a dark halo in the
Galaxy. For a simple isothermal halo, one can calculate that the minimum radial
extent is $\sim58$ kpc. We use our constraints on $\ve$ to determine the mass
of the Milky Way halo for three halo profiles. For example, an adiabatically
contracted NFW halo model results in a virial mass of
$1.42^{+1.14}_{-0.54}\times10^{12}M_\odot$ and virial radius of
$305^{+66}_{-45}$ kpc (90 per cent confidence). For this model the circular
velocity at the virial radius is $142^{+31}_{-21}\kms$. Although our halo
masses are model dependent, we find that they are in good agreement with each
other.
