Monte Carlo sampling of a Markov web

The efficiency of Markov-Chain Monte Carlo simulations can be enhanced by exploiting information about trial moves that would normally be rejected. The original presentation of this approach was limited to a specific MC sampling scheme. Here we present a general derivation of a method to improve the sampling efficiency of Monte Carlo simulations by collecting information about the microstates that can be linked directly to the sampled point via an independent Markov transition matrix. As an illustration, we show that our approach greatly enhances the efficiency of a scheme to compute the density of states of a square-well fluid.