Abstract
Systematic inaccuracy is inherent in any computational estimate of a nonlinear average, due to the availability of only a finite number of data values, [Formula presented]. Free energy differences [Formula presented] between two states or systems are critically important examples of such averages. Previous work has demonstrated, empirically, that the “finite-sampling error” can be very large—many times [Formula presented]—in [Formula presented] estimates for simple molecular systems. Here we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of [Formula presented] for large [Formula presented], the identification of a universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems.
| Original language | English (US) |
|---|---|
| Journal | Physical Review Letters |
| Volume | 89 |
| Issue number | 18 |
| DOIs | |
| State | Published - Jan 1 2002 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Theory of a Systematic Computational Error in Free Energy Differences. / Zuckerman, Daniel; Woolf, Thomas B.
In: Physical Review Letters, Vol. 89, No. 18, 01.01.2002.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Theory of a Systematic Computational Error in Free Energy Differences
AU - Zuckerman, Daniel
AU - Woolf, Thomas B.
PY - 2002/1/1
Y1 - 2002/1/1
N2 - Systematic inaccuracy is inherent in any computational estimate of a nonlinear average, due to the availability of only a finite number of data values, [Formula presented]. Free energy differences [Formula presented] between two states or systems are critically important examples of such averages. Previous work has demonstrated, empirically, that the “finite-sampling error” can be very large—many times [Formula presented]—in [Formula presented] estimates for simple molecular systems. Here we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of [Formula presented] for large [Formula presented], the identification of a universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems.
AB - Systematic inaccuracy is inherent in any computational estimate of a nonlinear average, due to the availability of only a finite number of data values, [Formula presented]. Free energy differences [Formula presented] between two states or systems are critically important examples of such averages. Previous work has demonstrated, empirically, that the “finite-sampling error” can be very large—many times [Formula presented]—in [Formula presented] estimates for simple molecular systems. Here we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of [Formula presented] for large [Formula presented], the identification of a universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems.
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U2 - 10.1103/PhysRevLett.89.180602
DO - 10.1103/PhysRevLett.89.180602
M3 - Article
VL - 89
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 18
ER -