The data augmentation algorithm

TL;DR

This paper provides a comprehensive review of data augmentation MCMC algorithms, covering their theoretical basis, implementation strategies, convergence properties, and applications in statistical inference.

Contribution

It synthesizes recent developments in DA MCMC algorithms, including convergence acceleration methods, extensions, and future research directions.

Findings

Survey of DA MCMC algorithms and their theoretical foundations

Strategies for improving convergence speed of DA algorithms

Extensions and future research directions in data augmentation methods

Abstract

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.