Abstract:

We propose a repulsiveattractive Metropolis algorithm that expedites a Markov chain's jumping between modes of a multimodal distribution in a simple and fast manner. This algorithm is essentially a MetropolisHastings algorithm with a proposal that consists of a downhill move in density that aims to make local modes repulsive, followed by an uphill move in density that aims to make local modes attractive. 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 downup 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 introduces a term that cancels with the intractable ratio. Using two examples, we demonstrate the potential for the proposed algorithm to explore a multimodal distribution more effectively and with less tuning than is commonly required by temperingbased methods.
