Here, ∆F h exact represents the exact free energy difference between the end states of the h-th path, and F h -1 -F h 1 is the estimated value. To ensure statistical robustness, we conduct 100 repetitions of the calculations, compute the mean RMSE over these repetitions, and perform paired t-tests to compare the three methods using the RMSEs obtained (Table and Figures ). Across all sample sizes n, CBayesMBAR has significantly smaller RMSEs compared to BayesMBAR and CCC, with p-values less than 10 -4 for all cases. Next, we assess the performance of the three methods in computing the free energy difference between the end states of individual paths using the mean absolute error (MAE) over the 100 repetitions as the metric (Table and Table ). In all cases, CBayesMBAR has the smallest MAEs among the three methods.