Efficient Simulation of Risk and Performance Measures, With Applications to the Design and Operation of Nuclear Power Plants

该合同为开发用于评估风险度量和其他性能度量的有效模拟方法提供了资金。研究的主要焦点是方差缩减技术（vrt），用于估计分位数和构建置信区间。分位数通常用于测量各种应用领域的风险。例如，核管理委员会（NRC）法规有时指定使用“95/95标准”来测量风险，这需要为0.95分位数计算95%的置信区间。为了满足美国核管理委员会的要求，从业人员目前采用粗糙的蒙特卡罗方法，这可能非常低效，因此，利用vrt构建分位数置信区间的研究有可能改变核工业中进行不确定性和安全性分析的方式。在金融领域，分位数被称为“风险价值”，银行规则将资本要求作为0.99分位数的函数给出。有效分位数估计的研究可以应用的其他领域包括项目规划、电信、制造、供应链和计算。如果成功，这项研究将产生新的模拟方法，以提高效率，有时是数量级，估计分位数和置信区间。在应用VRT时，置信区间的构建将涉及为VRT分位数估计器中出现的方差常数开发新的估计器。S中心极限定理。此外，还将研究建立分位数置信区间的其他技术。

This award provides funding for the development of efficient simulation methods for estimating risk measures and other performance metrics. A primary focus of the research is on variance-reduction techniques (VRTs) for estimating a quantile and constructing confidence intervals for it. Quantiles are commonly employed to measure risk in a diverse range of application areas. For example, Nuclear Regulatory Commission (NRC) regulations sometimes specify that risk is measured using a "95/95 criterion," which requires computing a 95% confidence interval for a 0.95-quantile. To satisfy the NRC requirements, practitioners currently resort to crude Monte Carlo, which can be hugely inefficient, so the research on constructing confidence intervals for quantiles with VRTs has the potential for altering the way uncertainty and safety analyses are performed in the nuclear industry. In finance, where a quantile is known as a "value-at-risk," there are banking rules for capital requirements given as a function of a 0.99-quantile. Other fields in which the research on efficient quantile estimation can be applied include project planning, telecommunications, manufacturing, supply chains, and computing. If successful, the research will yield new simulation methodologies to increase efficiency, sometimes by orders of magnitude, of estimators of quantiles and confidence intervals for them. The construction of confidence intervals when applying VRTs will involve developing new estimators for the variance constant appearing in the VRT quantile estimator?s central limit theorem. Moreover, other techniques for building confidence intervals for quantiles also will be investigated.