TY - JOUR

T1 - Systematic finite-sampling inaccuracy in free energy differences and other nonlinear quantities

AU - Zuckerman, Daniel M.

AU - Woolf, Thomas B.

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2004/3

Y1 - 2004/3

N2 - Systematic inaccuracy is inherent in any computational estimate of a non-linear average, such as the free energy difference ΔF between two states or systems, because of the availability of only a finite number of data values, N. In previous work, we outlined the fundamental statistical description of this "finite-sampling error." We now give a more complete presentation of (i) rigorous general bounds on the free energy and other nonlinear averages, which generalize Jensen's inequality; (ii) asymptotic N → ∞ expansions of the average behavior of the finite-sampling error in ΔF estimates; (iii) illustrative examples of large-N behavior, both in free-energy and other calculations; and (iv) the universal, large-N relation between the average finite-sampling error and the fluctuation in the error. An explicit role is played by Lévy and Gaussian limiting distributions.

AB - Systematic inaccuracy is inherent in any computational estimate of a non-linear average, such as the free energy difference ΔF between two states or systems, because of the availability of only a finite number of data values, N. In previous work, we outlined the fundamental statistical description of this "finite-sampling error." We now give a more complete presentation of (i) rigorous general bounds on the free energy and other nonlinear averages, which generalize Jensen's inequality; (ii) asymptotic N → ∞ expansions of the average behavior of the finite-sampling error in ΔF estimates; (iii) illustrative examples of large-N behavior, both in free-energy and other calculations; and (iv) the universal, large-N relation between the average finite-sampling error and the fluctuation in the error. An explicit role is played by Lévy and Gaussian limiting distributions.

KW - Finite-sampling error

KW - Free energy computation

KW - Jensen's inequality

KW - Nonlinear averages

KW - Systematic error

UR - http://www.scopus.com/inward/record.url?scp=3142740709&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3142740709&partnerID=8YFLogxK

U2 - 10.1023/b:joss.0000013961.84860.5b

DO - 10.1023/b:joss.0000013961.84860.5b

M3 - Article

AN - SCOPUS:3142740709

SN - 0022-4715

VL - 114

SP - 1303

EP - 1323

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 5-6

ER -