论文标题
使用数字和分布输入的计算机实验的设计和分析
Design and analysis of computer experiments with both numeral and distribution inputs
论文作者
论文摘要
如今，具有数字输入和分布输入的随机计算机模拟被广泛用于模拟包含大量不确定性的复杂系统。本文研究了此类计算机实验的设计和分析问题。首先，我们在概率度量空间中提供了有关Wasserstein距离的初步结果。 To handle the product space of the Euclidean space and the probability measure space, we prove that, through the mapping from a point in the Euclidean space to the mass probability measure at this point, the Euclidean space can be isomorphic to the subset of the probability measure space, which consists of all the mass measures, with respect to the Wasserstein distance.因此，可以将产品空间视为产品概率测量空间。我们得出了该产品概率测量空间的两个组成部分之间的瓦斯汀距离公式。其次，我们使用上述结果在欧几里得空间的产物空间和概率测量空间中构建基于Wasserstein的距离空间填充标准。提出了该产品空间中的一类最佳拉丁超管型设计。第三，我们提出了一个基于Wasserstein的基于距离的高斯过程模型，以分析具有数字输入和分布输入的计算机实验的数据。提出了在地铁模拟中的数值示例和实际应用，以显示我们方法的有效性。
Nowadays stochastic computer simulations with both numeral and distribution inputs are widely used to mimic complex systems which contain a great deal of uncertainty. This paper studies the design and analysis issues of such computer experiments. First, we provide preliminary results concerning the Wasserstein distance in probability measure spaces. To handle the product space of the Euclidean space and the probability measure space, we prove that, through the mapping from a point in the Euclidean space to the mass probability measure at this point, the Euclidean space can be isomorphic to the subset of the probability measure space, which consists of all the mass measures, with respect to the Wasserstein distance. Therefore, the product space can be viewed as a product probability measure space. We derive formulas of the Wasserstein distance between two components of this product probability measure space. Second, we use the above results to construct Wasserstein distance-based space-filling criteria in the product space of the Euclidean space and the probability measure space. A class of optimal Latin hypercube-type designs in this product space are proposed. Third, we present a Wasserstein distance-based Gaussian process model to analyze data from computer experiments with both numeral and distribution inputs. Numerical examples and real applications to a metro simulation are presented to show the effectiveness of our methods.
