A Gibbs sampler is a Markov chain Monte Carlo algorithm for obtaining a sequence of observations that are approximated from a specified multivariate probability distribution when direct sampling is difficult.
This sequence can be used to approximate the joint distribution, to approximate the marginal distribution of one of the variables, or a subset of variables, or to compute an integral.
Some of the variables correspond to observations whose values are known and therefore do not need to be sampled.
Gibbs sampling is commonly used as a means of statistical inference and in particular Bayesian inference.
It is a randomized algorithm and an alternative to deterministic algorithms for statistical inference such as the expectation maximization algorithm.
As with other MCMC algorithms, Gibbs sampling generates a Markov chain of samples, each correlated with nearby samples.
The Gibbs Sampling Algorithm is a particular instance of the Metropolis-Hastings Algorithm wherby every step is accepted.
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