Discussion of "Unbiased Markov chain Monte Carlo with couplings" by Pierre E. Jacob, John O'Leary and Yves F. Atchad\'e

TL;DR

This paper discusses the methodology of unbiased Markov chain Monte Carlo using couplings, providing insights and critiques on the original approach to enhance understanding and application.

Contribution

It offers a detailed discussion and critical analysis of the original unbiased MCMC with couplings, highlighting potential improvements and implications.

Findings

Clarifies the theoretical foundations of unbiased MCMC with couplings

Identifies limitations and proposes possible extensions

Enhances understanding of coupling strategies in MCMC

Abstract

This is a contribution for the discussion on "Unbiased Markov chain Monte Carlo with couplings" by Pierre E. Jacob, John O'Leary and Yves F. Atchad\'e to appear in the Journal of the Royal Statistical Society Series B.