BayesMBAR uses the posterior distribution (Eq. 3) to estimate the free energies and their uncertainties. Specifically, it estimates the free energy with either the mode or the mean of the posterior distribution, and computes the uncertainty of the estimate using the standard deviation of the posterior distribution. When the prior distribution p(F ) is chosen to be a uniform distribution, the mode of the posterior distribution is identical to the MBAR estimate. Our previous work has shown that BayesMBAR provides more accurate uncertainty estimates than the asymptotic analysis used in MBAR, especially when the number of configurations is small. 12 Futhermore, as a Bayesian method, BayesMBAR provides a principled way to incorporate prior information to improve the accuracy of free energy estimates. 12