Unbiased Markov chain Monte Carlo with couplings
Friday, October 13, 2017 - 3:30pm
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.
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