Coupling Control Variates for Markov Chain Monte Carlo

TL;DR

This paper introduces a novel coupling control variate method for Markov Chain Monte Carlo that enhances accuracy in cases where the stationary distribution is unknown, demonstrated through transport models.

Contribution

It generalizes control variates to Markov chains using couplings, improving MCMC accuracy without explicit knowledge of the stationary distribution.

Findings

Improved MCMC accuracy in certain models

Generalization of control variates for Markov chains

Effective in nonequilibrium transport models

Abstract

We show that Markov couplings can be used to improve the accuracy of Markov chain Monte Carlo calculations in some situations where the steady-state probability distribution is not explicitly known. The technique generalizes the notion of control variates from classical Monte Carlo integration. We illustrate it using two models of nonequilibrium transport.