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可用的系统中，量化不确定性影响的方法局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，在每个分层内采用拉丁超立方采样。通过基于广义多项式混沌展开与Sobol分解的局部（即与分层相关的）变异性指标引导先前估计，实现了序贯分层细化的自适应过程。对于给定的总样本数$N$，将相应分层构造的序贯分层采样估计与拉丁超立方采样进行适当平均，可得到方差降低的最终估计结果。数值实验表明该方法的有效性，在某些情况下可实现与$N^{-2}$成比例的方差衰减速度。