# Subsampling to Enhance Efficiency in Input Uncertainty Quantification

arXiv: https://arxiv.org/abs/1811.04500 · HTML: https://mlsanity.com/paper/1811.04500/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2018.

## Built on by (most cited first, 6 of 6)

- [Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networks](https://mlsanity.com/paper/2306.05674/) (2023)
- [Calibrating Over-Parametrized Simulation Models: A Framework via Eligibility Set](https://mlsanity.com/paper/2105.12893/) (2021)
- [Robust Output Analysis with Monte-Carlo Methodology](https://mlsanity.com/paper/2207.13612/) (2022)
- [Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty](https://mlsanity.com/paper/2404.19145/) (2024)
- [Ranking and Selection with Simultaneous Input Data Collection](https://mlsanity.com/paper/2503.11773/) (2025)
- [Quantifying and Attributing Submodel Uncertainty in Stochastic Simulation Models and Digital Twins](https://mlsanity.com/paper/2602.16099/) (2026)

## Abstract (arXiv)

In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the nonparametric setting, is commonly estimated via the bootstrap. However, due to the convolution of the simulation noise and the input noise, the bootstrap consists of a two-layer sampling and typically requires substantial simulation effort. This paper investigates a subsampling framework to reduce the required effort, by leveraging the form of the variance and its estimation error in terms of the data size and the sampling requirement in each layer. We show how the total required effort can be reduced from an order bigger than the data size in the conventional approach to an order independent of the data size in subsampling. We explicitly identify the procedural specifications in our framework that guarantee relative consistency in the estimation, and the corresponding optimal simulation budget allocations. We substantiate our theoretical results with numerical examples.