Uncertainty Quantification for Free Energy Calculations by Generalized Hierarchical Bayesian Inference

Free energy calculations are routinely used to study molecular processes inaccessible to unbiased molecular dynamics, but their utility ultimately depends on knowing when and how much their predictions can be trusted. Uncertainty estimation is therefore essential for distinguishing genuine physical features of a free energy profile from artifacts arising from limited simulation data or inadequate sampling. Gaussian processes have emerged as a powerful framework for reconstructing free energy profiles together with predictive uncertainties. However, existing implementations typically condition on fixed hyperparameters and observation noise, preventing predictive uncertainties from adapting to the information content of the simulation data. Here, we develop a generalized hierarchical Gaussian process framework that accounts for these neglected sources of uncertainty. Applications to umbrella sampling and extended Lagrangian metadynamics of peptide-lipid membrane interactions demonstrate that the resulting uncertainty estimates track reconstruction errors across a wide range of sampling and data conditions.