  We investigate the nature of nearby (10-15 kpc) high-speed stars in the Gaia
DR2 archive identified on the basis of parallax, proper motion and radial
velocity. Together with a consideration of their kinematic, orbital, and
photometric properties, we develop a novel strategy for evaluating whether high
speed stars are statistical outliers of the bound population or unbound stars
capable of escaping the Galaxy. Out of roughly 1.5 million stars with radial
velocities, proper motions, and 5-sigma parallaxes, we identify just over 100
high-speed stars. Of these, only two have a nearly 100% chance of being
unbound, with indication that they are not just bound outliers; both are likely
hyper-runaway stars. The rest of the high speed stars are likely statistical
outliers. We use the sample of high-speed stars to demonstrate that radial
velocity alone provides a poor discriminant of nearby, unbound stars. However,
nearby, unbound stars are efficiently identified from the tangential velocity,
using just parallax and proper motion. Within the full Gaia DR2 archive of
stars with 5-sigma parallax and proper motion but no radial velocity, we
identify a sample of 19 with speeds significantly larger than the local escape
speed of the Milky Way based on tangential motion alone.
