Talk by Prof. Pierre Jacob (Harvard University) on "Unbiased Markov chain Monte Carlo"

Prof. Pierre Jacob (Harvard University) will visit us on Feb 26 afternoon. If you are interested in chatting with him, please let me know (emtiyaz.khan [at] riken.jp).

Title: “Unbiased Markov chain Monte Carlo”

Abstract: 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 and Rhee (2014). The resulting unbiased estimators can be
computed independently on parallel processors. We discuss practical couplings for popular MCMC
algorithms. 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 toy examples, on an Ising model around its critical temperature, on a highdimensional variable selection problem, and on an approximation of the cut distribution arising in
Bayesian inference for models made of multiple modules.