(377g) Statistically Optimal Free Energy Estimates without Histograms

We present a maximum-likelihood method to combine data from multiple equilibrium simulations conducted at different thermodynamic states, based on statistical methods for correcting for biases in sampling [1]. The resulting estimator of the free energies yields the minimum-variance asymptotically unbiased estimate of the true free energy. This estimator is equivalent to multiple histogram method [2] or weighted histogram analysis method method [3] in the limit where the histogram bins are taken to be vanishingly small, but is derived without the need to invoke histograms, thus eliminating bias caused by binning. This is especially useful for highly multidimensional problems where histograms are difficult to populate.

Additionally, this method provides an estimator to directly compute uncertainties in the relative free energies from the data, something not possible with previous methods. This methodology is expected to be widely useful in the analysis of "alchemical" free energy calculations, generalized ensemble simulations, and the calculation of potentials of mean force.

[1] D. Gill, Y. Vardi, and J. A. Wellner , Annals of Stat. 16(3):1069-1112 (1988)

[2] A. M. Ferrenberg and R. H. Swendsen, Phys. Rev. Lett. 63:1195-1198 (1989)

[3] S. Kumar, D. Bouzida, R. H. Swendsen, P. A. Kollman and J. M. J. Rosenberg, J. Comput. Chem., 13, 1011-1021 (1992)