ADAPTIVE STRATIFIED SAMPLING FOR NONSMOOTH PROBLEMS

Science and engineering problems subject to uncertainty are frequently both computationally expensive feature nonsmooth parameter dependence, making standard Monte Carlo too slow, excluding efficient use of accelerated quantification methods relying on strict smoothness assumptions. To remedy these challenges, we propose an adaptive stratification method suitable for with significantly reduced variance compared sampling. The is iteratively refined samples added sequentially satisfy allocation criterion combining the benefits proportional optimal Theoretical estimates provided expected performance probability failure correctly estimate essential statistics. We devise a practical strata same kind geometrical shapes, cost-effective refinement satisfying greedy reduction criterion. A Python implementation presented methodology available at https://pypi.org/project/adaptive-stratification. Numerical experiments corroborate theoretical findings exhibit speedups up three orders magnitude