  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.
