Quantifying the Speed-Up from Non-Reversibility in MCMC Tempering Algorithms
Statistics Theory
2025-01-29 v1 Statistics Theory
Abstract
We investigate the increase in efficiency of simulated and parallel tempering MCMC algorithms when using non-reversible updates to give them "momentum". By making a connection to a certain simple discrete Markov chain, we show that, under appropriate assumptions, the non-reversible algorithms still exhibit diffusive behaviour, just on a different time scale. We use this to argue that the optimally scaled versions of the non-reversible algorithms are indeed more efficient than the optimally scaled versions of their traditional reversible counterparts, but only by a modest speed-up factor of about 42%.
Cite
@article{arxiv.2501.16506,
title = {Quantifying the Speed-Up from Non-Reversibility in MCMC Tempering Algorithms},
author = {Gareth O. Roberts and Jeffrey S. Rosenthal},
journal= {arXiv preprint arXiv:2501.16506},
year = {2025}
}