Taking bigger Metropolis steps by dragging fast variables

Abstract. I show how Markov chain sampling with the Metropolis-Hastings algorithm can be modified so as to take bigger steps when the distribution being sampled from has the characteristic that its density can be quickly recomputed for a new point if this point differs from a previous point only with respect to a subset of “fast ” variables. I show empirically that when using this method, the efficiency of sampling for the remaining “slow ” variables can approach what would be possible using Metropolis updates based on the marginal distribution for the slow variables.