Gibbs Sampler

Gibbs sampler, or a Gibbs sampling, is an algorithm for obtaining draws from a probability distribution using Markov chain Monte Carlo. Gibbs sampling is a special case of the Metropolis–Hastings algorithm where all samples are accepted, rather than going through an acceptance/rejection step. Commonly used for Bayesian statistics, Gibbs sampling is useful for approximating a complicated probability distribution that is either unknown or difficult to draw samples from directly (e.g., a posterior distribution); however, Gibbs sampling can also be used for known distributions. In addition to estimating being used for the estimation of model parameter, Gibbs samplers can also be used to simulate data from a set of known parameters.