论文标题
使用广义Lambda模型模仿随机模拟器
Emulation of stochastic simulators using generalized lambda models
论文作者
论文摘要
随机模拟器在许多应用科学和工程领域中无处不在。在不确定性量化和优化的背景下，通常需要大量模拟，这对于高保真模型变得很棘手。因此，在过去的十年中，已经对随机模拟器的替代模型进行了深入研究。在本文中，我们提出了一种新的方法，可以代理使用广义lambda分布的随机模拟器的响应分布，该分布的参数由模型输入的多项式混乱表示。与大多数现有方法相比，这种新方法在实验设计的每个点都不需要模拟器的复制运行。我们提出了一种新的拟合程序，将最大条件可能性估计与（修改）可行的概括最小二乘结合在一起。我们将我们的方法与最新的非参数内核估计进行了比较，该方法对数学金融和流行病学的四种不同应用。从随机模拟器的平均/方差和响应分布的均值/方差的准确性方面说明了其性能。由于所提出的方法也可以与包含复制的实验设计一起使用，因此我们对两个示例进行了比较，表明复制不一定有助于获得更好的总体准确性，甚至可能会使结果恶化（以固定的模拟器运行总数）。
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).
