We construct new estimates on the Galactic escape speed at various Galactocentric radii using the latest data release of the Radial Velocity Experiment (RAVE DR4). Compared to previous studies we have a database larger by a factor of 10 as well as reliable distance estimates for almost all stars. Our analysis is based on the statistical analysis of a rigorously selected sample of 90 high-velocity halo stars from RAVE and a previously published data set. We calibrate and extensively test our method using a suite of cosmological simulations of the formation of Milky Way-sized galaxies. Our best estimate of the local Galactic escape speed, which we define as the minimum speed required to reach three virial radii $R_{340}$, is $533^{+54}_{-41}$ km/s (90% confidence) with an additional 5% systematic uncertainty, where $R_{340}$ is the Galactocentric radius encompassing a mean over-density of 340 times the critical density for closure in the Universe. From the escape speed we further derive estimates of the mass of the Galaxy using a simple mass model with two options for the mass profile of the dark matter halo: an unaltered and an adiabatically contracted Navarro, Frenk & White (NFW) sphere. If we fix the local circular velocity the latter profile yields a significantly higher mass than the un-contracted halo, but if we instead use the statistics on halo concentration parameters in large cosmological simulations as a constraint we find very similar masses for both models. Our best estimate for $M_{340}$, the mass interior to $R_{340}$ (dark matter and baryons), is $1.3^{+0.4}_{-0.3} times 10^{12}$ M$_odot$ (corresponding to $M_{200} = 1.6^{+0.5}_{-0.4} times 10^{12}$ M$_odot$). This estimate is in good agreement with recently published independent mass estimates based on the kinematics of more distant halo stars and the satellite galaxy Leo I.
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