Riemannian Manifold Hamiltonian Monte Carlo

Understand

The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations.

• The method provides a fully automated adaptation mechanism that circumvents the costly pilot runs required to tune proposal densities for Metropolis-Hastings or indeed Hybrid Monte Carlo and Metropolis Adjusted Langevin Algorithms.
• This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain.
• The proposed method exploits the Riemannian structure of the parameter space of statistical models and thus automatically adapts to the local manifold structure at each step based on the metric tensor.