Unbiased Markov chain Monte Carlo with couplings

Abstract: Markov chain Monte Carlo methods provide consistent approximations of integrals as the number of iterations goes to infinity. However, these estimators are generally biased after any fixed number of iterations, which complicates both parallel computation. In this talk I will explain how to remove this burn-in  bias by using couplings of Markov chains and a telescopic sum argument, inspired by Glynn & Rhee (2014). The resulting unbiased estimators can be computed independently in parallel, and averaged. I will present coupling constructions for Metropolis-Hastings, Gibbs and Hamiltonian Monte Carlo. The proposed methodology will be illustrated on various examples. If time permits, I will describe how the proposed estimators can approximate the “cut” distribution that arises in Bayesian inference for misspecified models made of sub-models.

This is joint work with John O’Leary, Yves F. Atchade and Jeremy Heng,
available at arxiv.org/abs/1708.03625 and arxiv.org/abs/1709.00404.

Biography: Pierre Jacob is an Assistant Professor of Statistics at Harvard University since 2015. Pierre was before a postdoctoral research fellow at the University of Oxford and the National University of Singapore. His Ph.D. was from Université Paris-Dauphine on computational methods for Bayesian inference. His current research is on algorithms amenable to parallel computing for Bayesian inference and model comparison, with a focus on time series models.

Pierre E. Jacob
Assistant Professor of Statistics, Harvard University
personal website: sites.google.com/site/pierrejacob/
blog: statisfaction.wordpress.com/