Multipoint Metropolis Method with Application to Hybrid Monte Carlo

We propose the multipoint Metropolis algorithm as an extension of the orientational-bias Monte Carlo of Frenkel and Smit. A ratio statistics similar to that in the Metropolis algorithm is introduced to maintain the detailed balance. The multipoint idea can be applied to improve the efficiency of a general Markov chain-based Monte Carlo algorithm. To illustrate, we describe two variations of the idea—the random-grid Metropolis and the multipoint Hybrid Monte Carlo—and apply them to a number of examples.