Zusammenfassung
Markov chain Monte Carlo (MCMC) methods provide consistent of integrals as
the number of iterations goes to infinity. MCMC estimators are generally biased
after any fixed number of iterations. 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 in
parallel. 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 high-dimensional variable selection
problem, and on an approximation of the cut distribution arising in Bayesian
inference for models made of multiple modules.
Nutzer