Estimation via Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a powerful means for generating random samples that can be used in computing statistical estimates and marginal and conditional probabilities. MCMC methods rely on dependent (Markov) sequences having a limiting distribution corresponding to a distribution of interest. This article is a survey of popular implementations of MCMC, focusing particularly on the two most popular specific implementations of MCMC: Metropolis-Hastings (M-H) and Gibbs sampling. Our aim is to provide the reader with some of the central motivation and the rudiments needed for a straightforward application.