# Computing the variance of a conditional expectation via non-nested Monte Carlo

arXiv: https://arxiv.org/abs/1605.05454 · HTML: https://mlsanity.com/paper/1605.05454/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2016.

## Built on by (most cited first, 2 of 2)

- [Constructing unbiased gradient estimators with finite variance for conditional stochastic optimization](https://mlsanity.com/paper/2206.01991/) (2022)
- [Critical-State RL: Diagnosing Trainable States for Multi-Turn Tool Use](https://mlsanity.com/paper/2609.24985/) (2026)

## Abstract (arXiv)

Computing the variance of a conditional expectation has often been of importance in uncertainty quantification. Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call 1frac12-level simulation since the optimal inner-level sample size is bounded as the computational budget increases. In this letter we construct unbiased non-nested Monte Carlo estimators based on the so-called pick-freeze scheme due to Sobol'. An extension of our approach to compute higher order moments of a conditional expectation is also discussed.