Zuckerman Daniel M, Woolf Thomas B
Department of Physiology, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205, USA.
Phys Rev Lett. 2002 Oct 28;89(18):180602. doi: 10.1103/PhysRevLett.89.180602. Epub 2002 Oct 15.
Systematic inaccuracy is inherent in any computational estimate of a nonlinear average, due to the availability of only a finite number of data values, N. Free energy differences (Delta)F 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 k(B)T--in (Delta)F 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 1/N for large N, the identification of a universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems.
由于仅能获得有限数量的数据值(N)，任何非线性平均值的计算估计都存在系统性误差。两个状态或系统之间的自由能差(\Delta F)就是此类平均值的重要示例。先前的工作已通过实验证明，对于简单分子系统，在(\Delta F)估计中“有限采样误差”可能非常大——可达(k_BT)的许多倍。在此，我们给出了误差的理论描述，包括一个示例问题的精确解、大(N)时关于(1/N)的精确渐近行为、一条通用定律的确定以及数值示例。该理论依赖于对中心极限定理和其他极限定理的修正。
