We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up
by "splitting" the Hamiltonian in a way that allows much of the movement around
the state space to be done at low computational cost. One context where this is
possible is when the log density of the distribution of interest (the potential
energy function) can be written as the log of a Gaussian density, which is a
quadratic function, plus a slowly varying function. Hamiltonian dynamics for
quadratic energy functions can be analytically solved.