Bayesian Multistate Bennett Acceptance Ratio Methods

Abstract

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.

References in corpus (5)

• MCMC using Hamiltonian dynamics
• Statistically optimal analysis of samples from multiple equilibrium states
• Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise
• Free energy surface reconstruction from umbrella samples using Gaussian process regression
• Using reweighting and free energy surface interpolation to predict solid-solid phase diagrams