高阶路径积分中重加权采样的无效性和系统规模的灾难
The inefficiency of re-weighted sampling and the curse of system size in high order path integration
摘要：
通过对具有不同分布的一组样本进行统计重新加权来计算目标概率密度的平均值是一种在原子模拟和金融等不同领域中普遍采用的策略。在这里，我们提出了一个非常一般的分析这种方法的准确性和效率，突出了它的一些弱点。然后，我们给出了一个例子，我们的结果可以使用，特别是高阶路径积分方法的可行性评估。我们证明，这些技术中最有前途的-这是基于重新加权采样-是注定要失败的系统的大小增加，因为指数增长的统计不确定性的重新加权平均。
英文摘要：
Computing averages over a target probability density by statistical re-weighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we present a very general analysis of the accuracy and efficiency of this approach, highlighting some of its weaknesses. We then give an example of how our results can be used, specifically to assess the feasibility of high-order path integral methods. We demonstrate that the most promising of these techniques -- which is based on re-weighted sampling -- is bound to fail as the size of the system is increased, because of the exponential growth of the statistical uncertainty in the re-weighted average.
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