Abstract Statistical emulators are used to approximate the output of complex physical models when their computational burden limits any sensitivity and uncertainty analysis of model output to variation in the model inputs. In this paper, we introduce a flexible emulator which is able to handle multivariate model outputs and missing values. The emulator is based on a spatial model and the D-STEM software, which is extended to include emulator fitting using the EM algorithm. The missing values handling capabilities of the emulator are exploited to keep the number of model output realisations as low as possible when the computing burden of each realisation is high. As a case study, we emulate the output of the Atmospheric Dispersion Modelling System (ADMS) used by the Scottish Environment Protection Agency (SEPA) to model the air quality of the city of Aberdeen (UK). With the emulator, we study the city air quality under a discrete set of realisations and identify conditions under which, with a given probability, the 40 μ g m − 3 yearly average concentration limit for NO2 of EU legislation is not exceeded at the locations of the city monitoring stations. The effect of missing values on the emulator estimation and probability of exceedances are studied by means of simulations.

中文翻译：

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具有缺失值的多元模型输出的统计仿真器

摘要 当统计仿真器的计算负担限制了模型输出的任何敏感性和不确定性分析对模型输入变化的影响时，统计仿真器用于近似复杂物理模型的输出。在本文中，我们介绍了一个灵活的模拟器，它能够处理多变量模型输出和缺失值。模拟器基于空间模型和 D-STEM 软件，该软件经过扩展，包括使用 EM 算法的模拟器拟合。当每个实现的计算负担很高时，模拟器的缺失值处理能力被利用来保持模型输出实现的数量尽可能少。作为案例研究，我们模拟了苏格兰环境保护署 (SEPA) 使用的大气扩散建模系统 (ADMS) 的输出，以模拟阿伯丁市（英国）的空气质量。使用模拟器，我们研究了一组离散实现下的城市空气质量，并确定了在给定概率下，欧盟法规规定的 NO2 年平均浓度限值 40 μ gm − 3城市监测站。通过模拟研究了缺失值对模拟器估计和超出概率的影响。在城市监测站的位置，没有超过欧盟法律规定的 40 μ gm - 3 年平均 NO2 浓度限制。通过模拟研究了缺失值对模拟器估计和超出概率的影响。在城市监测站的位置，没有超过欧盟法律规定的 40 μ gm - 3 年平均 NO2 浓度限制。通过模拟研究了缺失值对模拟器估计和超出概率的影响。