Bayesian estimation of free energies from equilibrium simulations

Area of Science:

• Statistical physics
• Computational chemistry
• Biomolecular simulation

Background:

• Free energy calculations are crucial in statistical physics and biomolecular simulations.
• Existing methods for free energy estimation have limitations in scope and accuracy.

Purpose of the Study:

• To develop a novel Bayesian method for estimating free energies from equilibrium Monte Carlo simulations.
• To provide a unifying probabilistic framework for free energy calculations.

Main Methods:

• Developed a Gibbs sampler for efficient sampling of free energies and density of states.
• Utilized Bayesian inference for probabilistic estimation of free energy differences and uncertainties.

Main Results:

• The Gibbs sampler efficiently samples free energies and the density of states.
• The Bayesian method accurately estimates expected free energy differences and their uncertainties.
• Established that existing methods like WHAM and MBAR are approximations of this full probabilistic treatment.

Conclusions:

• The proposed Bayesian method offers a robust and unifying framework for free energy calculations.
• This approach enhances the accuracy and scope of free energy estimation in simulations.
• Provides a more rigorous foundation for biomolecular simulations and statistical physics studies.