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：多态本内特接受率（MBAR）方法是计算热力学态自由能的常用方法。本研究提出BayesMBAR，即MBAR方法的贝叶斯推广。通过将热力学态采样的构型与先验分布相结合，BayesMBAR可计算自由能的后验分布。基于后验分布，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，当采用均匀先验分布时，BayesMBAR可恢复MBAR的结果，但能提供更准确的不确定性估计。此外，若存在关于自由能的先验知识，BayesMBAR可通过非均匀先验分布将这些信息纳入估计过程。例如，通过引入自由能曲面光滑性的先验知识，BayesMBAR比MBAR方法能提供更准确的估计。鉴于MBAR在自由能计算中的广泛应用，我们预计BayesMBAR将成为各类自由能计算应用中的重要工具。