Convergence of Preconditioned Hamiltonian Monte Carlo on Hilbert Spaces

Hamiltonian Monte Carlo (HMC) is a a Markov Chain Monte Carlo (MCMC) method for sampling from complex probability measures whose normalizing constant is unknown. It originated under the name "Hybrid Monte Carlo" in Duane et al. (1987) in statistical physics. The'target' measure that HMC can sample from has the form dπ(q) exp( Φ(q)) dq, (1) i.e. the target measure has a positive density with respect to the Lebesgue measure dq. The means that the density of π w.r.t.