Equilibrium Free Energies from Nonequilibrium Measurements Using Maximum-Likelihood Methods

Michael R. Shirts, Eric Bair, Giles Hooker, and Vijay S. Pande
Phys. Rev. Lett. 91, 140601 – Published 2 October 2003
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Abstract

We present a maximum likelihood argument for the Bennett acceptance ratio method, and derive a simple formula for the variance of free energy estimates generated using this method. This derivation of the acceptance ratio method, using a form of logistic regression, a common statistical technique, allows us to shed additional light on the underlying physical and statistical properties of the method. For example, we demonstrate that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements.

  • Received 27 June 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.140601

©2003 American Physical Society

Authors & Affiliations

Michael R. Shirts

  • Department of Chemistry, Stanford University, Stanford, California 94305-5080, USA

Eric Bair and Giles Hooker

  • Department of Statistics, Stanford University, Stanford, California 94305-4065, USA

Vijay S. Pande

  • Department of Chemistry, Stanford University, Stanford, California 94305-5080, USA

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Issue

Vol. 91, Iss. 14 — 3 October 2003

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Heating up of Superconductors
January 27, 2017

This collection marks the 30th anniversary of the discovery of high-temperature superconductors. The papers selected highlight some of the advances that have been made to date, both in understanding why these compounds behave in the way they do, and in utilizing them in applications. The papers included in the collection have been made free to read.

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