Skew Brownian Motion and Complexity of the ALPS Algorithm
Probability
2021-05-13 v2 Computation
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.
Cite
@article{arxiv.2009.12424,
title = {Skew Brownian Motion and Complexity of the ALPS Algorithm},
author = {Gareth O. Roberts and Jeffrey S. Rosenthal and Nicholas G. Tawn},
journal= {arXiv preprint arXiv:2009.12424},
year = {2021}
}