Improving on the Independent Metropolis-Hastings algorithm

This paper proposes methods to improve Monte Carlo estimates when the Independent Metropolis-Hastings Algorithm (IMHA) is used. Our rst approach uses a control variate based on the sample generated by the proposal distribution. We derive the variance of our estimator for a xed sample size n and show that, as n tends to innit y, this variance is asymptotically smaller than the one obtained with the IMHA. Our second approach is based on Jensen's inequality. We use a Rao-Blackwellization and exploit the lack of symmetry in the IMHA. An upper bound on the improvements that we can obtain by these methods is derived.