  With its systematic exploration of probability distributions, Hamiltonian
Monte Carlo is a potent Markov Chain Monte Carlo technique; it is an approach,
however, ultimately contingent on the choice of a suitable Hamiltonian
function. By examining both the symplectic geometry underlying Hamiltonian
dynamics and the requirements of Markov Chain Monte Carlo, we construct the
general form of admissible Hamiltonians and propose a particular choice with
potential application in Bayesian inference.
