论文标题
多态顺序蒙特卡洛采样器进行不确定性定量
Multicanonical Sequential Monte Carlo Sampler for Uncertainty Quantification
论文作者
论文摘要
在许多实际工程系统中，系统的性能或可靠性以标量参数为特征。该性能参数的分布在许多不确定性量化问题中很重要，从风险管理到公用事业优化。实际上，此分布通常不能通过分析得出，必须通过模拟以数字获得。为此，经常使用标准的蒙特卡洛模拟，但是，它们无法有效地重建分布的尾巴，这在许多应用中都是必不可少的。一种可能的补救措施是使用多义蒙特卡洛法，这是一种自适应重要性采样方案。在这种方法中，人们从每种迭代中的非标准形式的重要性采样分布中绘制样本，通常是通过马尔可夫链蒙特卡洛（MCMC）完成的。 MCMC本质上是序列的，因此与并行性斗争。在本文中，我们提出了一种新方法，该方法使用顺序的蒙特卡洛采样器来借鉴重要性采样分布，这特别适合并行实现。通过数学和实际示例，我们证明了该方法的竞争性能。
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging from risk management to utility optimisation. In practice, this distribution usually cannot be derived analytically and has to be obtained numerically by simulations. To this end, standard Monte Carlo simulations are often used, however, they cannot efficiently reconstruct the tail of the distribution which is essential in many applications. One possible remedy is to use the Multicanonical Monte Carlo method, an adaptive importance sampling scheme. In this method, one draws samples from an importance sampling distribution in a nonstandard form in each iteration, which is usually done via Markov chain Monte Carlo (MCMC). MCMC is inherently serial and therefore struggles with parallelism. In this paper, we present a new approach, which uses the Sequential Monte Carlo sampler to draw from the importance sampling distribution, which is particularly suited for parallel implementation. With both mathematical and practical examples, we demonstrate the competitive performance of the proposed method.
