Hamiltonian-Assisted Metropolis Sampling

Various Markov chain Monte Carlo (MCMC) methods are studied to improve upon random walk Metropolis sampling, for simulation from complex distributions. Examples include Metropolis-adjusted Langevin algorithms, Hamiltonian Carlo, and other algorithms related underdamped dynamics. We propose a broad class of irreversible sampling called Hamiltonian-assisted (HAMS), develop two specific with appropriate tuning preconditioning strategies. Our HAMS designed simultaneously achieve distinctive properties, while using an augmented target density momentum as auxiliary variable. One is generalized detailed balance, which induces exploration the target. The rejection-free property Gaussian prespecified variance matrix. This allows our preconditioned perform satisfactorily relatively large step sizes. Furthermore, we formulate framework Metropolis–Hastings not only highlights construction at more abstract level, but also facilitates possible further development MCMC algorithms. present several numerical experiments, where proposed consistently yield superior results among existing same schemes.