Latin Hyperrectangle Sampling for Computer Experiments
Latin Hyperrectangle Sampling for Computer Experiments
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DOI：
10.1198/004017006000000101
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发表时间：
2006-11
期刊：
影响因子：
2.5
通讯作者：
David Mease;D. Bingham
中科院分区：
文献类型：
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作者：
David Mease;D. Bingham
拉丁超立方采样（LHS）是计算机实验中评估函数期望的流行方法。然而，当针对非均匀分布获取感兴趣的期望时，通常对概率空间的变换可能会导致相对平滑的函数在低概率区域变得极其可变。因此，超立方方法中固有的等概率单元通常倾向于对这些区域中总点的比例不足进行采样。本文介绍了拉丁超矩形采样 (LHRS)，它是 LHS 的推广，允许不相等的单元概率，以解决此问题。给出了许多示例，说明了所提出的方法相对于 LHS 在所得估计量的方差方面的改进。还描述了基于正交阵列的 LHS、分层 LHS 和置乱网络的扩展。
Latin hypercube sampling (LHS) is a popular method for evaluating the expectation of functions in computer experiments. However when the expectation of interest is taken with respect to a nonuniform distribution, the usual transformation to the probability space can cause relatively smooth functions to become extremely variable in areas of low probability. Consequently, the equal probability cells inherent in hypercube methods often tend to sample an insufficient proportion of the total points in these areas. This article introduces Latin hyperrectangle sampling (LHRS), a generalization of LHS that allows for nonequal cell probabilities, to address this problem. A number of examples are given illustrating the improvement of the proposed methodology over LHS with respect to the variance of the resulting estimators. Extensions to orthogonal array-based LHS, stratified LHS, and scrambled nets are also described.