Skew brownian motion and complexity of the alps algorithm

Abstract Simulated tempering is a popular method of allowing Markov chain Monte Carlo algorithms to move between modes multimodal target density $\pi$ . Tawn, Moores and Roberts (2021) introduces the Annealed Leap-Point Sampler (ALPS) allow for rapid movement modes. In this paper we prove that, under appropriate assumptions, suitably scaled version ALPS algorithm converges weakly skew Brownian motion. Our results show mixes in time $O(d [\log d]^2)$ or O ( d ), depending on which used.