In the field of sensitivity analysis, Sobol’ indices are widely used to assess the importance of the inputs of a model to its output. Among the methods that estimate these indices, the replication procedure is noteworthy for its efficient cost. A practical problem is how many model evaluations must be performed to guarantee a sufficient precision on the Sobol’ estimates. The present paper tackles this issue by rendering the replication procedure iterative. The idea is to enable the addition of new model evaluations to progressively increase the accuracy of the estimates. These evaluations are done at points located in under-explored regions of the experimental designs, but preserving their characteristics. The key feature of this approach is the construction of nested space-filling designs. For the estimation of first-order indices, a nested Latin hypercube design is used. For the estimation of closed second-order indices, two constructions of a nested orthogonal array design are proposed. Regularity and uniformity properties of the nested designs are studied.

在灵敏度分析领域，Sobol指数被广泛用于评估模型输入对其输出的重要性。在估计这些索引的方法中，复制过程因其有效成本而值得注意。一个实际的问题是必须执行多少个模型评估才能保证Sobol估算值具有足够的精度。本文通过使复制过程迭代来解决此问题。这样做的想法是能够添加新的模型评估，以逐步提高估计的准确性。这些评估是在实验设计的未充分研究区域中的点进行的，但要保留其特征。这种方法的关键特征是嵌套空间填充设计的构建。为了估算一阶指标，使用嵌套的拉丁超立方体设计。为了估计封闭的二阶指数，提出了嵌套正交阵列设计的两种构造。研究了嵌套设计的规则性和均匀性。