Physics (Internal)

"Unbiased Markov chain Monte Carlo with couplings joint work with John O'Leary, Yves F. Atchadé"

This event is part of the Condensed Matter Theory Seminar Series.

Markov chain Monte Carlo (MCMC) methods provide consistent approximations of integrals as the number of iterations goes to infinity. MCMC estimators are generally biased after any fixed number of iterations, which complicates both parallel computation and the construction of confidence intervals. We propose to remove this bias by using couplings of Markov chains together with a telescopic sum argument of Glynn & Rhee (2014). The resulting unbiased estimators can be computed in parallel, with confidence intervals following directly from the Central Limit Theorem for i.i.d. variables. We discuss practical couplings for popular algorithms such as Metropolis-Hastings, Gibbs samplers, and Hamiltonian Monte Carlo. We establish the theoretical validity of the proposed estimators and study their efficiency relative to the underlying MCMC algorithms. Finally, we illustrate the performance and limitations of the method on various examples, involving discrete and continuous high dimensional state spaces.