For this reason, we recommend against subsampling input data for the Bennett Acceptance Ratio (BAR) and the Multistate Bennett Acceptance Ratio (MBAR) free energy estimators. These are no longer the maximum likelihood free energy estimators when applied to correlated samples. Still, they remain robust estimators, and correcting for the correlation is unlikely to yield much improvement unless there are large differences in correlation between states. However, subsampling input for MBAR is often recommended because the asymptotic variance estimate given by Kong et al. and used in the original MBAR paper is derived for uncorrelated samples, meaning it is a large underestimate when there is substantial correlation. While subsampling decreases bias in this uncertainty estimate, it adds noise to the free energy and uncertainty estimates. A better approach may be to use an uncertainty estimator which accounts for correlation, for example, block bootstrapping, or a corrected asymptotic estimator. 61,64