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.

翻译：多态贝内特接受比（MBAR）方法是计算热力学态自由能的常用方法。本文提出了BayesMBAR，一种MBAR方法的贝叶斯推广。通过将热力学态采样的构象与先验分布相结合，BayesMBAR能够计算自由能的后验分布。利用该后验分布，我们推导出自由能估计值并计算其相关不确定性。值得注意的是，当使用均匀先验分布时，BayesMBAR可恢复MBAR的结果，但能提供更精确的不确定性估计。此外，当存在自由能的先验知识时，BayesMBAR可通过采用非均匀先验分布将这些信息纳入估计过程。例如，我们证明通过引入自由能曲面的光滑性先验知识，BayesMBAR能比MBAR方法提供更准确的估计。鉴于MBAR在自由能计算中的广泛应用，我们预期BayesMBAR将成为各类自由能计算应用中的关键工具。