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The level-based stratified sampling plan

机译：基于级别的分层抽样计划

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If the probability distribution of the input variable to a system described by a computer code is known, computer simulations can obtain the distribution function of the output variable. With a complicated program, each simulation can take a very long time. It thus is necessary to choose the combinations of the input parameters carefully to get as much information as possible with a small number of computer runs. Different methods for choosing the input parameters are described in the literature. As a criteria for a good sampling plan, unbiased estimates and low mean squared error are used. By computer experiments, it has been shown that he sampling plans based on Latin hypercubes often have the smallest variance of the estimated output variable. The author in this paper shows that a stratified sampling plan with strata defined by the surfaces in the sampling space were the output variable is constant has the lowest variance among all unbiased sampling plans. However, a serious disadvantage with this sampling plan is that it can be constructed only if the distribution to be estimated is fully known. The author then proposes a level based stratified sampling plan based on a simple approximation of the system. The first part of the article gives the mathematical background, and the last part gives an example of how the theory can be used in an engineering application.In Section 2, a property of the level-based stratified sampling plan is discussed. Theorems and lemmas are stated and their proofs are also given. Section 3 shows an application of how a level-based stratified sampling plan can be constructed for a simple model of a physical system with stochastic construction parameters. Discussion and conclusions are given in Section 4.
机译：如果已知输入变量到计算机代码描述的系统的概率分布，则计算机模拟可以获得输出变量的分布函数。使用复杂的程序，每个模拟都可能花费很长时间。因此，有必要仔细选择输入参数的组合，以在少量计算机运行时获得尽可能多的信息。在文献中描述了用于选择输入参数的不同方法。作为良好采样计划的标准，使用了无偏估计和低均方误差。通过计算机实验表明，他基于拉丁超立方体的采样计划通常具有估计的输出变量的最小方差。本文的作者表明，在所有无偏抽样方案中，具有由抽样空间中的表面定义的分层抽样方案（输出变量为常数）的分层抽样方案方差最小。但是，该采样计划的一个严重缺点是，只有在完全知道要估计的分布的情况下，才能构造它。然后，作者基于系统的简单近似值，提出了一个基于层次的分层抽样计划。本文的第一部分提供了数学背景，最后一部分给出了如何在工程应用中使用该理论的示例。在第二部分中，讨论了基于层次的分层抽样计划的属性。陈述定理和引理，并给出它们的证明。第3节显示了如何为具有随机构造参数的物理系统的简单模型构造基于层次的分层抽样计划的应用。讨论和结论在第4节中给出。

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