Quantifying the Speed-Up from Non-Reversibility in MCMC Tempering Algorithms

TL;DR

This paper analyzes how non-reversible updates in MCMC tempering algorithms can modestly improve efficiency by approximately 42%, by connecting their behavior to a simple Markov chain and examining diffusive properties.

Contribution

It demonstrates that non-reversible MCMC tempering algorithms achieve a modest efficiency gain over reversible ones through a theoretical analysis of their diffusive behavior.

Findings

Non-reversible algorithms exhibit diffusive behavior on a different time scale.

Optimal scaling of non-reversible algorithms leads to about 42% speed-up.

Theoretical connection to a simple Markov chain explains efficiency improvements.

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%.