Editing Gibbs sampling (section)

{{short description|Monte Carlo algorithm}}
{{Bayesian statistics}}

In [[statistics]], '''Gibbs sampling''' or a '''Gibbs sampler''' is a [[Markov chain Monte Carlo]] (MCMC) [[algorithm]] for sampling from a specified [[multivariate distribution|multivariate]] [[probability distribution]] when direct sampling from the joint distribution is difficult, but sampling from the [[Conditional probability distribution|conditional distribution]] is more practical.  This sequence can be used to approximate the joint distribution (e.g., to generate a histogram of the distribution); to approximate the [[marginal distribution]] of one of the variables, or some subset of the variables (for example, the unknown [[parameter]]s or [[latent variable]]s); or to compute an [[integral]] (such as the [[expected value]] of one of the variables).  Typically, some of the variables correspond to observations whose values are known, and hence do not need to be sampled.

Gibbs sampling is commonly used as a means of [[statistical inference]], especially [[Bayesian inference]].  It is a [[randomized algorithm]] (i.e. an algorithm that makes use of [[random number generation|random number]]s), and is an alternative to [[deterministic algorithm]]s for statistical inference such as the [[expectation–maximization algorithm]] (EM).

As with other MCMC algorithms, Gibbs sampling generates a [[Markov chain]] of samples, each of which is [[autocorrelation|correlated]] with nearby samples. As a result, care must be taken if independent samples are desired. Samples from the beginning of the chain (the ''burn-in period'') may not accurately represent the desired distribution and are usually discarded.