We present a maximum likelihood argument for the Bennett acceptance ratio method, and derive a simple formula for the variance of free energy estimates generated using this method. This derivation of the acceptance ratio method, using a form of logistic regression, a common statistical technique, allows us to shed additional light on the underlying physical and statistical properties of the method. For example, we demonstrate that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements.

• Received 27 June 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.140601