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- Title
Skew brownian motion and complexity of the alps algorithm.
- Authors
Roberts, Gareth O.; Rosenthal, Jeffrey S.; Tawn, Nicholas G.
- Abstract
Simulated 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.
- Subjects
MARKOV chain Monte Carlo; ALGORITHMS; PROBABILITY theory; COMPUTATIONAL complexity; BROWNIAN motion
- Publication
Journal of Applied Probability, 2022, Vol 59, Issue 3, p777
- ISSN
0021-9002
- Publication type
Article
- DOI
10.1017/jpr.2021.78