A Bayesian approach to calculating free energies in chemical and biological systems

A common objective of molecular simulations in chemistry and biology is to calculate the free energy difference between systems of interest. We propose to improve estimates of these free energies by modeling the underlying probability distribution as a the square of a "wave function", which is a linear combination of Gram-Charlier polynomials. The number of terms, N, in this expansion is determined by calculating the posterior probability, P(N X), where X stands for all energy differences sampled in a simulation. The method offers significantly improved free energy estimates when the probability distribution is broad and non-Gaussian, which makes it applicable to challenging problems, such as protein-drug interactions.