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Performing numerical integration when the integrand itself cannot beevaluated point-wise is a challenging task that arises in statistical analysis,notably in Bayesian inference for models with intractable likelihood functions.Markov chain Monte Carlo (MCMC) algorithms have been proposed for this setting,such as the pseudo-marginal method for latent variable models and the exchangealgorithm for a class of undirected graphical models. As with any MCMCalgorithm, the resulting estimators are justified asymptotically in the limitof the number of iterations, but exhibit a bias for any fixed number ofiterations due to the Markov chains starting outside of stationarity. This"burn-in" bias is known to complicate the use of parallel processors for MCMCcomputations. We show how to use coupling techniques to generate unbiasedestimators in finite time, building on recent advances for generic MCMCalgorithms. We establish the theoretical validity of some of these proceduresby extending existing results to cover the case of polynomially ergodic Markovchains. The efficiency of the proposed estimators is compared with that ofstandard MCMC estimators, with theoretical arguments and numerical experimentsincluding state space models and Ising models.

Unbiased Markov chain Monte Carlo for intractable target distributions