Sequential Monte Carlo for rare event estimation
Sequential Monte Carlo for rare event estimation
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DOI：
10.1007/s11222-011-9231-6
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发表时间：
2012-05-01
影响因子：
2.2
通讯作者：
Guyader, A.
中科院分区：
文献类型：
--
作者：
Cerou, F.;Del Moral, P.;Guyader, A.
本文讨论了一种新的策略来模拟罕见的事件和相关的蒙特卡罗估计的尾部概率。我们的方法使用一个相互作用的粒子系统，并利用该系统的费曼-卡茨表示来分析它们的波动。我们精确的分析标准的多级分裂算法的方差揭示了一个改进的机会。这导致了一种新的方法，依赖于自适应水平，并产生，在一个理想化的版本的算法的限制，估计与最佳方差。这项理论工作的动机来自数字内容的水印和指纹识别中出现的问题，这代表了稀有事件模拟技术应用的一个新领域。一些数值结果表明，这些实际应用中的性能接近我们的技术的理想版本。
This paper discusses a novel strategy for simulating rare events and an associated Monte Carlo estimation of tail probabilities. Our method uses a system of interacting particles and exploits a Feynman-Kac representation of that system to analyze their fluctuations. Our precise analysis of the variance of a standard multilevel splitting algorithm reveals an opportunity for improvement. This leads to a novel method that relies on adaptive levels and produces, in the limit of an idealized version of the algorithm, estimates with optimal variance. The motivation for this theoretical work comes from problems occurring in watermarking and fingerprinting of digital contents, which represents a new field of applications of rare event simulation techniques. Some numerical results show performance close to the idealized version of our technique for these practical applications.