Skew brownian motion and complexity of the alps algorithm
Copyright policy )Skew brownian motion and complexity of the alps algorithm
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.
FOS: Computer and information sciences, generator, skew Brownian motion, Probability (math.PR), diffusion limit, Statistics - Computation, Markov chain Monte Carlo, Discrete-time Markov processes on general state spaces, Computational methods in Markov chains, ALPS algorithm, FOS: Mathematics, Continuous-time Markov processes on general state spaces, Brownian motion, QA, Mathematics - Probability, Computation (stat.CO)
FOS: Computer and information sciences, generator, skew Brownian motion, Probability (math.PR), diffusion limit, Statistics - Computation, Markov chain Monte Carlo, Discrete-time Markov processes on general state spaces, Computational methods in Markov chains, ALPS algorithm, FOS: Mathematics, Continuous-time Markov processes on general state spaces, Brownian motion, QA, Mathematics - Probability, Computation (stat.CO)
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