  Riemann manifold Hamiltonian Monte Carlo (RMHMC) has the potential to produce
high-quality Markov chain Monte Carlo-output even for very challenging target
distributions. To this end, a symmetric positive definite scaling matrix for
RMHMC, which derives, via a modified Cholesky factorization, from the
potentially indefinite negative Hessian of the target log-density is proposed.
The methodology is able to exploit the sparsity of the Hessian, stemming from
conditional independence modeling assumptions, and thus admit fast
implementation of RMHMC even for high-dimensional target distributions.
Moreover, the methodology can exploit log-concave conditional target densities,
often encountered in Bayesian hierarchical models, for faster sampling and more
straight forward tuning. The proposed methodology is compared to alternatives
for some challenging targets, and is illustrated by applying a state space
model to real data.
