Optimal estimators and asymptotic variances for nonequilibrium path-ensemble averages
Optimal estimators and asymptotic variances for nonequilibrium path-ensemble averages
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DOI：
10.1063/1.3242285
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发表时间：
2009-10-07
影响因子：
4.4
通讯作者：
Chodera, John D.
中科院分区：
文献类型：
--
作者：
Minh, David D. L.;Chodera, John D.
现有的非平衡路径集合平均值的最佳估计器被证明属于扩展桥采样的框架内。使用这个框架，我们推导出一个通用的最小方差估计器，它可以结合从多个路径集合采样的非平衡轨迹数据来估计非平衡期望的任意函数。该框架还用于获得渐近方差估计，这是统计不确定性的有用度量。特别是，我们开发了与 Jarzynski 自由能等式相关的渐近方差估计和根据单向或双向路径样本计算的平均力势的 Hummer-Szabo 表达式。这些估计器在单分子拉伸实验模型中得到了证明。在这些模拟中，发现当偏差较小时，渐近方差表达式可以准确地表征估计量周围的置信区间。因此，对于具有较大偏差的单向估计，置信区间的描述不准确，但对于该模型，它很大程度上反映了 Minh 和 Adib 导出的双向估计量中的真实误差。 (C) 2009 年美国物理研究所。 [doi:10.1063/1.3242285]
Existing optimal estimators of nonequilibrium path-ensemble averages are shown to fall within the framework of extended bridge sampling. Using this framework, we derive a general minimal-variance estimator that can combine nonequilibrium trajectory data sampled from multiple path-ensembles to estimate arbitrary functions of nonequilibrium expectations. The framework is also applied to obtain asymptotic variance estimates, which are a useful measure of statistical uncertainty. In particular, we develop asymptotic variance estimates pertaining to Jarzynski's equality for free energies and the Hummer-Szabo expressions for the potential of mean force, calculated from uni- or bidirectional path samples. These estimators are demonstrated on a model single-molecule pulling experiment. In these simulations, the asymptotic variance expression is found to accurately characterize the confidence intervals around estimators when the bias is small. Hence, the confidence intervals are inaccurately described for unidirectional estimates with large bias, but for this model it largely reflects the true error in a bidirectional estimator derived by Minh and Adib. (C) 2009 American Institute of Physics. [doi:10.1063/1.3242285]