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Quantifying the Speed-Up from Non-Reversibility in MCMC Tempering Algorithms
Gareth O. Roberts, Jeffrey S. Rosenthal · 2025-01-28 · via math.ST updates on arXiv.org

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%.

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