Unbiased Markov chain Monte Carlo with couplings

Friday, October 13, 2017 - 3:30pm

Pierre Jacob, Harvard University


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. 


Seminars generally take place in 116 Old Chemistry Building on Fridays from 3:30 - 4:30 pm. For additional information contact: karen.whitesell@duke.edu or phone 919-684-8029. Sorry, but we do not have reprints available. Please feel free to contact the authors by email for follow-up information, articles, etc. Reception following seminar in 211 Old Chemistry

Old Chemistry 116

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