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arXiv · 2009.12424

Skew Brownian Motion and Complexity of the ALPS Algorithm

Gareth O. Roberts·Jeffrey S. Rosenthal·Nicholas G. Tawn
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Abstract

Simulated tempering is a popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. 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.

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Gareth O. Roberts, Jeffrey S. Rosenthal, Nicholas G. Tawn. 2020-09-25. Skew Brownian Motion and Complexity of the ALPS Algorithm. https://arxiv.org/abs/2009.12424

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