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The data augmentation algorithm

arXiv 2406.10464 ↗First posted 15 Jun 2024stat.CO stat.ME stat.MLcited by 0

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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.

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References · 12

  1. 2015Fast Moment-Based Estimation for Hierarchical Modelscited by 4
  2. 2017Scaling up Data Augmentation MCMC via Calibrationcited by 4
  3. 2021Divide-and-Conquer Bayesian Inference in Hidden Markov Modelscited by 3
  4. 2017Estimating the spectral gap of a trace-class Markov operatorcited by 2
  5. 2017Consistent estimation of the spectrum of trace class data augmentation algorithmscited by 2
  6. 2018An Asynchronous Distributed Expectation Maximization Algorithm For Massive Data: The DEM Algorithmcited by 2
  7. 2021Asynchronous and Distributed Data Augmentation for Massive Data Settingscited by 2
  8. 2016Convergence properties of Gibbs samplers for Bayesian probit regression with proper priorscited by 1
  9. 2017A novel sandwich algorithm for empirical Bayes analysis of rank datacited by 1
  10. 2019Fast Markov chain Monte Carlo for high dimensional Bayesian regression models with shrinkage priorscited by 1
  11. 2021Block Gibbs samplers for logistic mixed models: convergence properties and a comparison with full Gibbs samplerscited by 1
  12. 2022MCMC for GLMMscited by 1

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