Systematic Finite-Sampling Inaccuracy in Free Energy Differences and Other Nonlinear Quantities

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Systematic inaccuracy is inherent in any computational estimate of a non-linear average, such as the free energy difference (Delta-F) 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 underscore the universality of the phenomenon; (ii) asymptotic N->infinity expansions of the average behavior of the finite-sampling error in Delta-F 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 Levy and Gaussian limiting distributions.
Version to appear in J. Stat. Phys. -- only minor corrections

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Computational Physics, Chemical Physics, Data Analysis, Statistics and Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/84852

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/physics/0208015
 http://arxiv.org/abs/physics/0208015

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arXiv