Mathematics of importance: The optimal importance sampling algorithm for estimating the probability of a black swan event.

罕见事件模拟和建模对于我们理解核事故、自然灾害和金融危机等高成本、难以预测的事件至关重要。对此类高影响事件进行定量分析，需要准确估计此类罕见事件发生的概率。在现实模型中，这种概率很难估计，因为没有精确的简单的分析公式，现有的估计方法也非常失败。迫切需要一种新的有效的方法。本项目开发了一种新的蒙特卡罗方法，将能够可靠和准确地估计罕见事件的概率。

Rare event simulation and modelling is critical to our understanding of high-cost hard-to-predict events such as nuclear accidents, natural disasters, and financial crises. Quantitative analysis of such high-impact events demands the accurate estimation of the probability of occurrence of such rare events. In realistic models this probability is very difficult to estimate, because exact simple analytical formulas are not available and the existing estimation methods fail spectacularly. There is an urgent need for new efficient methodology. This project develops a new Monte Carlo method that will be able to estimate reliably and accurately rare-event probabilities.