# The data augmentation algorithm

arXiv: https://arxiv.org/abs/2406.10464 · HTML: https://mlsanity.com/paper/2406.10464/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 75 references that are in the map.
- First posted on arXiv 15 Jun 2024.

## Builds on (most cited first, 12 of 12)

- [Fast Moment-Based Estimation for Hierarchical Models](https://mlsanity.com/paper/1504.04941/) (2015)
- [Scaling up Data Augmentation MCMC via Calibration](https://mlsanity.com/paper/1703.03123/) (2017)
- [Divide-and-Conquer Bayesian Inference in Hidden Markov Models](https://mlsanity.com/paper/2105.14395/) (2021)
- [Estimating the spectral gap of a trace-class Markov operator](https://mlsanity.com/paper/1704.00850/) (2017)
- [Consistent estimation of the spectrum of trace class data augmentation algorithms](https://mlsanity.com/paper/1711.00572/) (2017)
- [An Asynchronous Distributed Expectation Maximization Algorithm For Massive Data: The DEM Algorithm](https://mlsanity.com/paper/1806.07533/) (2018)
- [Asynchronous and Distributed Data Augmentation for Massive Data Settings](https://mlsanity.com/paper/2109.08969/) (2021)
- [Convergence properties of Gibbs samplers for Bayesian probit regression with proper priors](https://mlsanity.com/paper/1602.08558/) (2016)
- [A novel sandwich algorithm for empirical Bayes analysis of rank data](https://mlsanity.com/paper/1708.04377/) (2017)
- [Fast Markov chain Monte Carlo for high dimensional Bayesian regression models with shrinkage priors](https://mlsanity.com/paper/1903.06964/) (2019)
- [Block Gibbs samplers for logistic mixed models: convergence properties and a comparison with full Gibbs samplers](https://mlsanity.com/paper/2101.03849/) (2021)
- [MCMC for GLMMs](https://mlsanity.com/paper/2204.01866/) (2022)

## Abstract (arXiv)

The data augmentation (DA) algorithms are popular Markov chain Monte Carlo (MCMC) algorithms often used for sampling from intractable probability distributions. This review article comprehensively surveys DA MCMC algorithms, highlighting their theoretical foundations, methodological implementations, and diverse applications in frequentist and Bayesian statistics. The article discusses tools for studying the convergence properties of DA algorithms. Furthermore, it contains various strategies for accelerating the speed of convergence of the DA algorithms, different extensions of DA algorithms and outlines promising directions for future research. This paper aims to serve as a resource for researchers and practitioners seeking to leverage data augmentation techniques in MCMC algorithms by providing key insights and synthesizing recent developments.