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Abstract:
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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 due to Glynn & Rhee (2014). The resulting procedure produces unbiased estimators (exact estimation) without the requirement of perfect sampling. Furthermore, it can be readily implemented in parallel, with confidence intervals following directly from the Central Limit Theorem for i.i.d. variables. We illustrate the performance and limitations of the approach on various problems. (Joint work with Pierre Jacob (Harvard), and John O’leary (Harvard).
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