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.

引入BayesMBAR作为MBAR方法的贝叶斯推广，在计算热力学状态的自由能值时，通过将采样自热力学状态的构型与先验分布整合，计算出自由能的后验分布，并通过后验分布得出自由能估计和估计误差。BayesMBAR能够提供比MBAR方法更准确的不确定性估计，同时也可以整合关于自由能的先验知识，提供更准确的估计结果，并有望成为自由能计算的重要工具。

贝叶斯多状态贝内特接受比率方法