CBayesMBAR is built upon the Bayesian multistate Bennett acceptance ratio (BayesMBAR) method, a Bayesian generalization of the multistate Bennett acceptance ratio (MBAR) method. In BayesMBAR, we formulate free energy estimation as a Bayesian inference problem and derive a posterior distribution of free energy differences given sampled configurations. This posterior distribution is then used to estimate free energy differences and their uncertainties. The Bayesian framework of BayesMBAR naturally facilitates the coupling of multiple BayesMBAR calculations on a perturbation graph with cycles. Here, we first briefly review the BayesMBAR method and then explain how to couple multiple BayesMBAR calculations in CBayesMBAR using the cycle consistency condition.