Skew Brownian Motion and Complexity of the ALPS Algorithm

09/25/2020

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by   Gareth O. Roberts, et al.

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Simulated tempering is a popular method of allowing MCMC algorithms to move between modes of a multimodal target density π. The paper [24] introduced the Annealed Leap-Point Sampler (ALPS) to allow for rapid movement between modes. In this paper, we prove that, under appropriate assumptions, a suitably scaled version of the ALPS algorithm converges weakly to skew Brownian motion. Our results show that under appropriate assumptions, the ALPS algorithm mixes in time O(d[log(d)]^2 ) or O(d), depending on which version is used.