For BayesMBAR, we independently compute free energy differences for each path, using the posterior mode as the free energy estimate and the standard deviation of the posterior distribution (estimated from 1000 samples) as the uncertainty. For CCC, we adjust the free energy differences obtained with BayesMBAR to satisfy the cycle consistency condition (details are in the Supporting Information). For CBayesMBAR, we simultaneously estimate free energy differences across all paths, coupling the calculations using the cycle consistency condition. As with BayesMBAR, we use the posterior mode for the free energy estimate and the standard deviation of the posterior distribution (estimated from 1000 samples) for uncertainty quantification.