The Level-Based Stratified Sampling Plan
基于输出等值面的分层抽样设计AI 解读 ↓
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基于输出等值面的分层抽样设计
- 研究问题
- 当计算机模型每次运行成本很高时，如何安排输入抽样，以较少模拟获得输出分布信息并降低估计方差？
- 方法与思路
- 作者以输出恒定的等值面定义分层，研究理想抽样设计，再利用近似解构造可行方案，并以粗细有限元模型说明应用。
- 材料陈述的贡献
- 摘要称，所述等值面分层在其无偏抽样设计比较中具有最低方差，但精确构造需要已知解，因此另讨论近似实施。
- 阅读关注点
- 阅读全文时应核对最低方差结论对应的估计对象、预算与比较范围，以及近似等值面如何影响无偏性和方差表现。
- 阅读边界
- 仅据稿件版本未注明的索引摘要；精确最优设计依赖已知解，近似方案的误差与成本未说明，不能将其同等视为最优。
原文摘要
If the probability distribution of the input variables to a system described by a computer code is known, the distribution function of the output variable can be obtained by computer simulations. With a complicated program, each simulation can take 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 (true random sampling, stratified sampling, Latin hypercube sampling, and updated Latin hypercube sampling) 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 the sampling plans based on Latin hypercubes often have the smallest variance of the estimated output variable. In this article it is shown that a stratified sampling plan with strata defined by the surfaces in the sampling space where the output variable is constant has the lowest variance among all unbiased sampling plans. Unfortunately, it is possible to construct the sampling plan only if the solution is already available. However, an approximate sampling plan can be constructed if an approximate solution is known. In an application, it is shown how the results from a finite element method (FEM) model with a coarse element structure can be used to construct a sampling plan to be used with a FEM model with a finer element structure.