# Missing at random: a stochastic process perspective

arXiv: https://arxiv.org/abs/1801.06739 · HTML: https://mlsanity.com/paper/1801.06739/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2018.

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

- [Multiple imputation and test-wise deletion for causal discovery with incomplete cohort data](https://mlsanity.com/paper/2108.13331/) (2021)
- [High-Dimensional Gaussian Mean Estimation under Realizable Contamination](https://mlsanity.com/paper/2603.16798/) (2026)

## Abstract (arXiv)

We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing data framework, we give a novel characterisation of the observed data as a stopping-set sigma algebra. We demonstrate that the usual missingness at random conditions are equivalent to requiring particular stochastic processes to be adapted to a set-indexed filtration of the complete data: measurability conditions that suffice to ensure the likelihood factorisation necessary for ignorability. Our rigorous statement of the missing at random conditions also clarifies a common confusion: what is fixed, and what is random?