  The Hamiltonian Monte Carlo (HMC) method allows sampling from continuous
densities. Favorable scaling with dimension has led to wide adoption of HMC by
the statistics community. Modern auto-differentiating software should allow
more widespread usage in Bayesian inverse problems. This paper analyzes the two
major difficulties encountered using HMC for inverse problems: poor
conditioning and multi-modality. Novel results on preconditioning and replica
exchange Monte Carlo parameter selection are presented in the context of
spectroscopy. Recommendations are analyzed rigorously in the Gaussian case, and
shown to generalize in a fusion plasma reconstruction.
