Quantifying the effect of uncertainties in systems where only point evaluations in the stochastic domain but no regularity conditions are available is limited to sampling-based techniques. This work presents an adaptive sequential stratification estimation method that uses Latin Hypercube Sampling within each stratum. The adaptation is achieved through a sequential hierarchical refinement of the stratification, guided by previous estimators using local (i.e., stratum-dependent) variability indicators based on generalized polynomial chaos expansions and Sobol decompositions. For a given total number of samples $N$, the corresponding hierarchically constructed sequence of Stratified Sampling estimators combined with Latin Hypercube sampling is adequately averaged to provide a final estimator with reduced variance. Numerical experiments illustrate the procedure's efficiency, indicating that it can offer a variance decay proportional to $N^{-2}$ in some cases.

翻译：在仅能对随机域进行点评估且无正则性条件的系统中，量化不确定性效应受限于基于采样的技术。本文提出一种自适应序贯分层估计方法，在每一层内采用拉丁超立方体抽样。该自适应过程通过分层序贯细化实现，其细化方向由基于广义多项式混沌展开和Sobol分解的局部（即层依赖）变异性指标引导的前期估计器决定。对于给定总样本数$N$，将相应分层构建的序贯分层估计序列与拉丁超立方体抽样适当平均，从而得到方差减小的最终估计量。数值实验证明了该方法的有效性，表明在某些情况下可实现与$N^{-2}$成比例的方差衰减。