Title: Subsampling MCMC - an Introduction for the Survey Statistician

Author(s): Khue-Dung Dang, Matias Quiroz, Mattias Villani, Minh-Ngoc Tran and Robert Kohn
Issue: Volume 80 Series A Part 3 Year 2018
Pages: 33 -- 69
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.
Primary 62-02; Secondary 62D05
Keywords and phrases: Pseudo-Marginal MCMC, Difference estimator, Hamiltonian Monte Carlo (HMC)