Reweighting from the mixture distribution as a better way to describe the Multistate Bennett Acceptance Ratio

The multistate Bennett Acceptance Ratio is provably the lowest variance unbiased estimator of both free energies and ensemble averages, and has a number of important advantages over previous methods, such as WHAM. Despite its advantages, the original MBAR paper was rather dense and mathematically complicated, limiting the extent to which people could expand and apply it. We present here a different way to think about MBAR that is much more intuitive and makes it clearer why the method works so well.