Although the Metropolis algorithm is simple to implement, it often has
difficulties exploring multimodal distributions. We propose the
repelling-attracting Metropolis (RAM) algorithm that maintains the
simple-to-implement nature of the Metropolis algorithm, but is more likely to
jump between modes. The RAM algorithm is a Metropolis-Hastings algorithm with a
proposal that consists of a downhill move in density that aims to make local
modes repelling, followed by an uphill move in density that aims to make local
modes attracting. The downhill move is achieved via a reciprocal Metropolis
ratio so that the algorithm prefers downward movement. The uphill move does the
opposite using the standard Metropolis ratio which prefers upward movement.
This down-up movement in density increases the probability of a proposed move
to a different mode. Because the acceptance probability of the proposal
involves a ratio of intractable integrals, we introduce an auxiliary variable
which creates a term in the acceptance probability that cancels with the
intractable ratio. Using several examples, we demonstrate the potential for the
RAM algorithm to explore a multimodal distribution more efficiently than a
Metropolis algorithm and with less tuning than is commonly required by
tempering-based methods.

本文提出了一种名为 RAM 算法的 Metropolis-Hastings 算法，它具有维持简单实现的 Metropolis 算法的特性，但更容易在多峰分布中跳跃。该算法利用在密度下降时使局部模式斥力并在密度上升时使局部模式吸引的提议，从而增加了跳跃到不同模式的概率。通过引入一个辅助变量来消除难以积分的比率项，展示了 RAM 算法在探索多峰分布方面比调质法更有效。