2023/05/22 by Sebastian Krumscheid, Krumscheid, Sebastian, Per Pettersson +1 · 1 citation
Decision Sciences · Engineering · #Control Systems and Identification #FOS: Computer and information sciences #Fault Detection and Control Systems #Methodology (stat.ME) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2305.13421
openalex publication_date 2023/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.