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一般正交阵列空间填充设计的中心极限定理AI 解读

Orthogonal array based space-filling designs (Owen [Statist. Sinica 2 (1992a) 439–452]; Tang [J. Amer. Statist. Assoc. 88 (1993) 1392–1397]) have become popular in computer experiments, numerical integration, stochastic optimization and uncertainty quantification. As improvements of ordinary Latin hypercube designs, these designs achieve stratification in multi-dimensions. If the underlying orthogonal array has strength $t$, such designs achieve uniformity up to $t$ dimension…

切片拉丁超立方设计AI 解读

This article proposes a method for constructing a new type of space-filling design, called a sliced Latin hypercube design, intended for running computer experiments. Such a design is a special Latin hypercube design that can be partitioned into slices of smaller Latin hypercube designs. It is desirable to use the constructed designs for collective evaluations of computer models and ensembles of multiple computer models. The proposed construction method is easy to implement,…

大规模计算机实验的高精度模拟器AI 解读

Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the procedure shows substantial improvements in overall accuracy, but its theoretical properties are not well established. We introduce the terms nominal and numeric error and decompose the overall error of an interpolator into nominal and…

嵌套格点抽样：随机化嵌套正交表的新抽样方案AI 解读

A nested orthogonal array is an orthogonal array that contains a smaller orthogonal array as a subarray. We construct a new sampling scheme, called nested lattice sampling, by randomizing nested orthogonal arrays with nested permutations. For a pair of nested lattice samples associated with a nested orthogonal array of strength t, the points in both samples achieve uniformity in t or lower dimensions. Some statistical properties of nested lattice samples based on strength…