# Subsampling MCMC - An introduction for the survey statistician

arXiv: https://arxiv.org/abs/1807.08409 · HTML: https://mlsanity.com/paper/1807.08409/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2018.

## Built on by (most cited first, 7 of 7)

- [Bayesian inference via sparse Hamiltonian flows](https://mlsanity.com/paper/2203.05723/) (2022)
- [Fast Bayesian Coresets via Subsampling and Quasi-Newton Refinement](https://mlsanity.com/paper/2203.09675/) (2022)
- [Coreset Markov Chain Monte Carlo](https://mlsanity.com/paper/2310.17063/) (2023)
- [Machine Learning and the Future of Bayesian Computation](https://mlsanity.com/paper/2304.11251/) (2023)
- [General bounds on the quality of Bayesian coresets](https://mlsanity.com/paper/2405.11780/) (2024)
- [How To Train Your Program: a Probabilistic Programming Pattern for Bayesian Learning From Data](https://mlsanity.com/paper/2105.03650/) (2021)
- [Predictive Coresets](https://mlsanity.com/paper/2502.05725/) (2025)

## Abstract (arXiv)

The rapid development of computing power and efficient Markov Chain Monte Carlo (MCMC) simulation algorithms have revolutionized Bayesian statistics, making it a highly practical inference method in applied work. However, MCMC algorithms tend to be computationally demanding, and are particularly slow for large datasets. Data subsampling has recently been suggested as a way to make MCMC methods scalable on massively large data, utilizing efficient sampling schemes and estimators from the survey sampling literature. These developments tend to be unknown by many survey statisticians who traditionally work with non-Bayesian methods, and rarely use MCMC. Our article explains the idea of data subsampling in MCMC by reviewing one strand of work, Subsampling MCMC, a so called pseudo-marginal MCMC approach to speeding up MCMC through data subsampling. The review is written for a survey statistician without previous knowledge of MCMC methods since our aim is to motivate survey sampling experts to contribute to the growing Subsampling MCMC literature.