Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling
Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling
复制标题
DOI：
10.1214/13-sts443
复制
发表时间：
2013-02
影响因子：
5.7
通讯作者：
Roman Schefzik;T. Thorarinsdottir;T. Gneiting
中科院分区：
文献类型：
--
作者：
Roman Schefzik;T. Thorarinsdottir;T. Gneiting
关键的决策往往依赖于复杂的计算机模拟模型的高维输出，这些模型显示出复杂的交叉变量、空间和时间依赖结构，天气和气候预测就是关键的例子。有一个强烈的认识，需要在这样的设置不确定性量化，为此，我们提出并审查了一个一般的多阶段的程序，称为系综copula耦合（ECC），进行如下：1。生成一个原始集合，由计算机模型的多个运行组成，这些运行以适当的方式在输入或模型参数方面有所不同。2.应用统计后处理技术，如贝叶斯模型平均或非齐次回归，以校正原始集合中的系统误差，从而分别获得每个单变量输出变量的校准和尖锐的预测分布。3.从每个后处理的预测分布中抽取样本。4.在原始系综的秩序结构中重新排列采样值以获得ECC后处理系综。在过去的十年里，集合和统计后处理的使用已经成为天气预报的常规。我们发现，看似无关的，最近的进展可以解释，融合和巩固的ECC的框架内，共同的线程是通过的经验copula的原始合奏。根据在采样阶段使用的分位数、随机抽取或变换，我们分别区分了ECC-Q、ECC-R和ECC-T变体。我们还描述了Schaake洗牌和现存的copula为基础的技术的关系。在一个案例研究中，ECC的方法被应用到温度，压力，降水和风超过德国的预测，基于50个成员的欧洲中期天气预报中心（ECMWF）合奏。
Critical decisions frequently rely on high-dimensional output from complex computer simulation models that show intricate cross-variable, spatial and temporal dependence structures, with weather and climate predictions being key examples. There is a strongly increasing recognition of the need for uncertainty quantification in such settings, for which we propose and review a general multi-stage procedure called ensemble copula coupling (ECC), proceeding as follows: 1. Generate a raw ensemble, consisting of multiple runs of the computer model that differ in the inputs or model parameters in suitable ways. 2. Apply statistical postprocessing techniques, such as Bayesian model averaging or nonhomogeneous regression, to correct for systematic errors in the raw ensemble, to obtain calibrated and sharp predictive distributions for each univariate output variable individually. 3. Draw a sample from each postprocessed predictive distribution. 4. Rearrange the sampled values in the rank order structure of the raw ensemble to obtain the ECC postprocessed ensemble. The use of ensembles and statistical postprocessing have become routine in weather forecasting over the past decade. We show that seemingly unrelated, recent advances can be interpreted, fused and consolidated within the framework of ECC, the common thread being the adoption of the empirical copula of the raw ensemble. Depending on the use of Quantiles, Random draws or Transformations at the sampling stage, we distinguish the ECC-Q, ECC-R and ECC-T variants, respectively. We also describe relations to the Schaake shuffle and extant copula-based techniques. In a case study, the ECC approach is applied to predictions of temperature, pressure, precipitation and wind over Germany, based on the 50-member European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble.