使用广义λ模型的随机模拟器的仿真
Emulation of stochastic simulators using generalized lambda models
摘要：
随机模拟器在应用科学和工程的许多领域中是普遍存在的。在不确定性量化和优化的背景下，大量的模拟通常是必要的，这对于高保真模型变得棘手。因此，代理模型的随机模拟器已被深入研究，在过去的十年。在本文中，我们提出了一种新的方法来替代的随机模拟器，它使用广义λ分布，其参数表示的多项式混沌扩展的模型输入的响应分布。与大多数现有方法相反，这种新方法不需要在试验设计的每个点重复运行模拟器。我们提出了一个新的拟合过程，结合最大条件似然估计（修改）可行的广义最小二乘。我们比较我们的方法与国家的最先进的非参数核估计四个不同的应用程序源于数学金融和流行病学。它的性能示出的随机模拟器和响应分布的均值/方差的准确性。由于所提出的方法也可以用于包含重复的试验设计，我们进行了比较的两个例子，表明重复不一定有助于获得更好的整体精度，甚至可能恶化的结果（在一个固定的总运行次数的模拟器）。
英文摘要：
Stochastic simulators are ubiquitous in many fields of applied sciences and engineering. In the context of uncertainty quantification and optimization, a large number of simulations is usually necessary, which becomes intractable for high-fidelity models. Thus surrogate models of stochastic simulators have been intensively investigated in the last decade. In this paper, we present a novel approach to surrogating the response distribution of a stochastic simulator which uses generalized lambda distributions, whose parameters are represented by polynomial chaos expansions of the model inputs. As opposed to most existing approaches, this new method does not require replicated runs of the simulator at each point of the experimental design. We propose a new fitting procedure which combines maximum conditional likelihood estimation with (modified) feasible generalized least-squares. We compare our method with state-of-the-art nonparametric kernel estimation on four different applications stemming from mathematical finance and epidemiology. Its performance is illustrated in terms of the accuracy of both the mean/variance of the stochastic simulator and the response distribution. As the proposed approach can also be used with experimental designs containing replications, we carry out a comparison on two of the examples, showing that replications do not necessarily help to get a better overall accuracy and may even worsen the results (at a fixed total number of runs of the simulator).
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