Journal of Applied Probability | VOL. 59
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Skew brownian motion and complexity of the alps algorithm

Publication Date Jul 12, 2022

Abstract

AbstractSimulated tempering is a popular method of allowing Markov chain Monte Carlo algorithms to move between modes of a multimodal target density $\pi$ . Tawn, Moores and Roberts (2021) introduces 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.

Concepts

Skew Brownian Motion Markov Chain Monte Carlo Algorithms Multimodal Density Complexity Of Algorithm Version Of Algorithm Multimodal Target Monte Carlo Algorithms Target Density Rapid Movement Brownian Motion

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