  Geodesic Monte Carlo (gMC) is a powerful algorithm for Bayesian inference on
non-Euclidean manifolds. The original gMC algorithm was cleverly derived in
terms of its progenitor, the Riemannian manifold Hamiltonian Monte Carlo
(RMHMC). Here, it is shown that alternative and theoretically simpler
derivations are available in which the original algorithm is a special case of
two general classes of algorithms characterized by non-trivial mass matrices.
The proposed derivations work entirely in embedding coordinates and thus
clarify the original algorithm as applied to manifolds embedded in Euclidean
space.
