## Non-reversibly updating a uniform [0,1] value
for Metropolis accept/reject decisions

**Radford M. Neal,
Dept. of Statistical Sciences and
Dept. of Computer Science, University of Toronto, Vector Institute Affiliate**

I show how it can be beneficial to express
Metropolis accept/reject decisions in terms of comparison with a
uniform [0,1] value, *u*, and to then update *u* non-reversibly, as
part of the Markov chain state, rather than sampling it independently
each iteration. This provides a small improvement for random walk
Metropolis and Langevin updates in high dimensions. It produces a
larger improvement when using Langevin updates with persistent
momentum, giving performance comparable to that of Hamiltonian Monte
Carlo (HMC) with long trajectories. This is of significance when some
variables are updated by other methods, since if HMC is used, these
updates can be done only between trajectories, whereas they can be
done more often with Langevin updates. I demonstrate that for a
problem with some continuous variables, updated by HMC or Langevin
updates, and also discrete variables, updated by Gibbs sampling
between updates of the continuous variables, Langevin with persistent
momentum and non-reversible updates to *u* samples nearly a factor of
two more efficiently than HMC. Benefits are also seen for a Bayesian
neural network model in which hyperparameters are updated by Gibbs
sampling.

Technical report, 31 January 2020, 14 pages:
pdf.

Also available as
arXiv:2001.11950.