The Hamiltonian Monte Carlo (HMC) method is a widely used Markov Chain Monte Carlo algorithm that offers the possibility of combining high acceptance rates and nonlocal moves. Most of the computational complexity of HMC lies in the numerical solution of a system of Hamiltonian differential equations and therefore it is of interest to identify the most efficient integrator. At present, the leapfrog/Verlet algorithm is the integrator of choice. In the talk I will explain the specific features of HMC that explain the succes of leapgrog, but I will also show that, in many problems, one may construct substantially better integrators that, while being esay to code, provide important computational savings.
Invited by Sebastian Reich