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Sampling from hierarchical Bayesian models is often difficult for MCMCmethods, because of the strong correlations between the model parameters andthe hyperparameters. Recent Riemannian manifold Hamiltonian Monte Carlo (RMHMC)methods have significant potential advantages in this setting, but arecomputationally expensive. We introduce a new RMHMC method, which we callsemi-separable Hamiltonian Monte Carlo, which uses a specially designed massmatrix that allows the joint Hamiltonian over model parameters andhyperparameters to decompose into two simpler Hamiltonians. This structure isexploited by a new integrator which we call the alternating blockwise leapfrogalgorithm. The resulting method can mix faster than simpler Gibbs samplingwhile being simpler and more efficient than previous instances of RMHMC.

Semi-Separable Hamiltonian Monte Carlo for Inference in Bayesian Hierarchical Models