  Hamiltonian Monte Carlo is a popular sampling technique for smooth target
densities. The scale lengths of the target have long been known to influence
integration error and sampling efficiency. However, quantitative measures
intrinsic to the target have been lacking. In this paper, we restrict attention
to the multivariate Gaussian and the leapfrog integrator, and obtain a
condition number corresponding to sampling efficiency. This number, based on
the spectral and Schatten norms, quantifies the number of leapfrog steps needed
to efficiently sample. We demonstrate its utility by using this condition
number to analyze HMC preconditioning techniques. We also find the condition
number of large inverse Wishart matrices, from which we derive burn-in
heuristics.
