Geometric integrators and the Hamiltonian Monte Carlo method

摘要: This paper surveys in detail the relations between numerical integration and Hamiltonian (or hybrid) Monte Carlo method (HMC). Since computational cost of HMC mainly lies integrations, these should be performed as efficiently possible. However, requires methods that have geometric properties being volume-preserving reversible, this limits number integrators may used. On other hand, important quantitative implications on error, which turn an impact acceptance rate proposal. While at present velocity Verlet algorithm is choice for good reasons, we argue can improved upon. We also discuss behavior dimensionality target distribution increases.