  We calculate radiative and collisional energy loss of hard partons traversing
the quark-gluon plasma created at RHIC and compare the respective size of these
contributions. We employ the AMY formalism for radiative energy loss and
include additionally energy loss by elastic collisions. Our treatment of both
processes is complete at leading order in the coupling, and accounts for the
probabilistic nature of jet energy loss. We find that a solution of the
Fokker-Planck equation for the probability density distributions of partons is
necessary for a complete calculation of the nuclear modification factor
$R_{AA}$ for pion production in heavy ion collisions. It is found that the
magnitude of $R_{AA}$ is sensitive to the inclusion of both collisional and
radiative energy loss, while the average energy is less affected by the
addition of collisional contributions. We present a calculation of $R_{AA}$ for
$\pi^0$ at RHIC, combining our energy loss formalism with a relativistic
(3+1)-dimensional hydrodynamic description of the thermalized medium.
