  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 Monte
Carlo, and other recent algorithms related to underdamped Langevin dynamics. We
propose a broad class of irreversible sampling algorithms, called Hamiltonian
assisted Metropolis sampling (HAMS), and develop two specific algorithms with
appropriate tuning and preconditioning strategies. Our HAMS algorithms are
designed to achieve two distinctive properties, while using an augmented target
density with momentum as an auxiliary variable. One is generalized detailed
balance, which induces an irreversible exploration of the target. The other is
a rejection-free property, which allows our algorithms to perform
satisfactorily with relatively large step sizes. Furthermore, we formulate a
framework of generalized Metropolis--Hastings sampling, which not only
highlights our construction of HAMS at a more abstract level, but also
facilitates possible further development of irreversible MCMC algorithms. We
present several numerical experiments, where the proposed algorithms are found
to consistently yield superior results among existing ones.
