Optimal input potential functions in the interacting particle system method
Optimal input potential functions in the interacting particle system method
复制标题
相互作用粒子系统方法中的最优输入势函数
DOI：
10.1137/050640667
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
J. Garnier
中科院分区：
文献类型：
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作者：
H. Chraibi;A. Dutfoy;T. Galtier;J. Garnier
用朴素的蒙特-卡罗方法评估罕见事件的概率是计算密集型的，因此需要更快的估计或方差减少方法。我们专注于这些方法之一，这是相互作用粒子系统（IPS）的方法。该方法是不是侵入性的意义上说，所考虑的随机马尔可夫系统模拟其原始分布，但选择步骤，有利于轨迹（粒子）具有高的潜在价值。一个无偏估计减少方差，然后可以提出。该方法需要指定一组势函数。这些函数的选择至关重要，因为它决定了方差减少的幅度。到目前为止，很少有关于如何选择潜在功能的信息。本文给出了使IPS方法估计量的渐近方差最小的最优势函数的表达式，并对势函数的实际设计提出了建议。
The assessment of the probability of a rare event with a naive Monte-Carlo method is computationally intensive, so faster estimation or variance reduction methods are needed. We focus on one of these methods which is the interacting particle system (IPS) method. The method is not intrusive in the sense that the random Markov system under consideration is simulated with its original distribution, but selection steps are introduced that favor trajectories (particles) with high potential values. An unbiased estimator with reduced variance can then be proposed. The method requires to specify a set of potential functions. The choice of these functions is crucial, because it determines the magnitude of the variance reduction. So far, little information was available on how to choose the potential functions. This paper provides the expressions of the optimal potential functions minimizing the asymptotic variance of the estimator of the IPS method and it proposes recommendations for the practical design of the potential functions.
DOI：
10.1137/18m1212100
发表时间：
2020
期刊：
Multiscale modeling & simulation : a SIAM interdisciplinary journal
影响因子：
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作者：
Aristoff D;Zuckerman DM
通讯作者：
Zuckerman DM