# Sequential Estimation using Hierarchically Stratified Domains with Latin Hypercube Sampling

arXiv: https://arxiv.org/abs/2305.13421 · HTML: https://mlsanity.com/paper/2305.13421/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2023.

## Built on by (most cited first, 1 of 1)

- [Enabling stratified sampling in high dimensions via nonlinear dimensionality reduction](https://mlsanity.com/paper/2506.08921/) (2025)

## Abstract (arXiv)

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.