The celebrated Hamilton Monte Carlo (HMC) algorithm is a powerful tool in computational statistics for sampling from intractable probability distributions. While HMC on Euclidean space is well-developed, implementing HMC on more general manifolds remains a major challenge. We propose an efficient HMC algorithm for symmetric spaces, employing Cartan geometry and reduction theory for Hamiltonian dynamics on a principal bundle. We validate our findings by implementation on a simulated dataset.
