The Geometry of Hamiltonian Monte Carlo

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.