Bayesian estimation of free energies from equilibrium simulations

Free energy calculations are an important tool in statistical physics and biomolecular simulation. This Letter outlines a Bayesian method to estimate free energies from equilibrium Monte Carlo simulations. A Gibbs sampler is developed that allows efficient sampling of free energies and the density of states. The Gibbs sampling output can be used to estimate expected free energy differences and their uncertainties. The probabilistic formulation offers a unifying framework for existing methods such as the weighted histogram analysis method and the multistate Bennett acceptance ratio; both are shown to be approximate versions of the full probabilistic treatment