The Geometry of Hamiltonian Monte Carlo

Given its systematic exploration, Hamiltonian Monte Carlo is a potent Markov Chain Monte Carlo technique. This approach, however, is 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.