# Median of Means Sampling for the Keister Function

arXiv: https://arxiv.org/abs/2501.10440 · HTML: https://mlsanity.com/paper/2501.10440/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 13 Jan 2025.

## Abstract (arXiv)

This study investigates the performance of median-of-means sampling compared to traditional mean-of-means sampling for computing the Keister function integral using Randomized Quasi-Monte Carlo (RQMC) methods. The research tests both lattice points and digital nets as point distributions across dimensions 2, 3, 5, and 8, with sample sizes ranging from 2^8 to 2^19 points. Results demonstrate that median-of-means sampling consistently outperforms mean-of-means for sample sizes larger than 10^3 points, while mean-of-means shows better accuracy with smaller sample sizes, particularly for digital nets. The study also confirms previous theoretical predictions about median-of-means' superior performance with larger sample sizes and reflects the known challenges of maintaining accuracy in higher-dimensional integration. These findings support recent research suggesting median-of-means as a promising alternative to traditional sampling methods in numerical integration, though limitations in sample size and dimensionality warrant further investigation with different test functions and larger parameter spaces.