Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods

Summary The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis–Hastings or indeed Hamiltonian 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…

• EA
  Engineering and Physical Sciences Research Council

  Awards: EP/F009429/1, EP/F009429/1, EP/E052029/1, EP/E052029/1, EP/E052029/2
• BA
  Biotechnology and Biological Sciences Research Council

  Awards: BB/G006997/1, BB/G006997/1