  We consider how different choices of kinetic energy in Hamiltonian Monte
Carlo affect algorithm performance. To this end, we introduce two quantities
which can be easily evaluated, the composite gradient and the implicit noise.
Results are established on integrator stability and geometric convergence, and
we show that choices of kinetic energy that result in heavy-tailed momentum
distributions can exhibit an undesirable negligible moves property, which we
define. A general efficiency-robustness trade off is outlined, and
implementations which rely on approximate gradients are also discussed. Two
numerical studies illustrate our theoretical findings, showing that the
standard choice which results in a Gaussian momentum distribution is not always
optimal in terms of either robustness or efficiency.
