Bayesian Multistate Bennett Acceptance Ratio Methods
This work addresses the need for better uncertainty quantification in free energy calculations, which is incremental but important for applications in fields like computational chemistry and biophysics.
The authors tackled the problem of estimating free energies and their uncertainties in thermodynamic states by introducing BayesMBAR, a Bayesian generalization of the multistate Bennett acceptance ratio (MBAR) method. The result shows that BayesMBAR provides more accurate uncertainty estimates than MBAR when using a uniform prior and improves accuracy by incorporating prior knowledge, such as smoothness of free energy surfaces.
The multistate Bennett acceptance ratio (MBAR) method is a prevalent approach for computing free energies of thermodynamic states. In this work, we introduce BayesMBAR, a Bayesian generalization of the MBAR method. By integrating configurations sampled from thermodynamic states with a prior distribution, BayesMBAR computes a posterior distribution of free energies. Using the posterior distribution, we derive free energy estimations and compute their associated uncertainties. Notably, when a uniform prior distribution is used, BayesMBAR recovers the MBAR's result but provides more accurate uncertainty estimates. Additionally, when prior knowledge about free energies is available, BayesMBAR can incorporate this information into the estimation procedure by using non-uniform prior distributions. As an example, we show that, by incorporating the prior knowledge about the smoothness of free energy surfaces, BayesMBAR provides more accurate estimates than the MBAR method. Given MBAR's widespread use in free energy calculations, we anticipate BayesMBAR to be an essential tool in various applications of free energy calculations.