Implementation of Nonreversible Metropolis-Hastings algorithms

Abstract

Metropolis-Hastings algorithm which keeps the detailed balance is the basic element for most Markov chain Monte Carlo sampling algorithms in which undermined Markov processes are reversible. Previous research shows that nonreversible Markov processes have a faster rate of convergence than reversible ones. Taking advantage of the “lifting” idea, this paper develops a general framework for designing Metropolis-Hastings algorithms breaking detailed balance and implements two new nonreversible Metropolis-Hastings algorithms based on the Gaussian proposal conditional probability and Langevin dynamics in the zero-mass limit respectively. Numerical simulations in one and two dimensions demonstrate that new nonreversible Metropolis-Hastings algorithms can speed up the convergence to target stationary distributions, which supports the theoretical finding and the design of our new algorithms.