Markov Chain Monte Carlo Methods
Siddhartha Chib · The New Palgrave Dictionary of Economics · 2008
MCMC methods, an important class of Monte Carlo methods, have played a major role in the growth of Bayesian statistics and econometrics. In an MCMC simulation, one samples a given distribution (say the posterior distribution in a Bayesian model) by simulating a suitably constructed Markov chain whose invariant distribution is the target distribution. The Metropolis–Hastings algorithm and its special case, the Gibbs sampler, are two common ways of devising an MCMC simulation. We discuss how these methods originate, discuss implementation issues and provide examples. The use of MCMC methods in Bayesian prediction and model choice problems is also discussed.