  We investigate the effect of using local and non-local second derivative
information on the performance of Hamiltonian Monte Carlo (HMC) sampling
methods, for high-dimension non-Gaussian distributions, with application to
Bayesian inference and nonlinear inverse problems. The Riemannian Manifold
Hamiltonian Monte Carlo (RMHMC) method uses second and third derivative
information to improve the performance of the HMC approach. We propose using
the local Hessian information at the start of each iteration, instead of
re-calculating the higher order derivatives in all sub-steps of the leapfrog
updating algorithm. We compare the result of Hessian-informed HMC method using
the local and nonlocal Hessian information, in a test bed of a high-dimensional
log-normal distribution, related to a problem of inferring soil properties.
