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
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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 -