# Tight relative estimation in the mean of Bernoulli random variables

arXiv: https://arxiv.org/abs/2210.12861 · HTML: https://mlsanity.com/paper/2210.12861/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 16 references that are in the map.
- First posted on arXiv 23 Oct 2022.

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

- [What Are the Odds? Improving the foundations of Statistical Model Checking](https://mlsanity.com/paper/2404.05424/) (2024)

## Abstract (arXiv)

Given a stream of Bernoulli random variables, consider the problem of estimating the mean of the random variable within a specified relative error with a specified probability of failure. Until now, the Gamma Bernoulli Approximation Scheme (GBAS) was the method that accomplished this goal using the smallest number of average samples. In this work, a new method is introduced that is faster when the mean is bounded away from zero. The process uses a two-stage process together with some simple inequalities to get rigorous bounds on the error probability.