11 Facts About Gibbs sampling

In statistics, Gibbs sampling or a Gibbs sampler is a Markov chain Monte Carlo algorithm for obtaining a sequence of observations which are approximated from a specified multivariate probability distribution, when direct sampling is difficult.

Gibbs sampling is commonly used as a means of statistical inference, especially Bayesian inference.

Gibbs sampling is named after the physicist Josiah Willard Gibbs, in reference to an analogy between the sampling algorithm and statistical physics.

Gibbs sampling is applicable when the joint distribution is not known explicitly or is difficult to sample from directly, but the conditional distribution of each variable is known and is easy to sample from.

The Gibbs sampling algorithm generates an instance from the distribution of each variable in turn, conditional on the current values of the other variables.

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Gibbs sampling is particularly well-adapted to sampling the posterior distribution of a Bayesian network, since Bayesian networks are typically specified as a collection of conditional distributions.

Gibbs sampling, in its basic incarnation, is a special case of the Metropolis–Hastings algorithm.

The point of Gibbs sampling is that given a multivariate distribution it is simpler to sample from a conditional distribution than to marginalize by integrating over a joint distribution.

Essential ingredients of the Gibbs sampling sampler is the -th full conditional posterior distribution for each.

However, in the particular case that the child nodes are discrete, Gibbs sampling is feasible, regardless of whether the children of these child nodes are continuous or discrete.

Gibbs sampling will become trapped in one of the two high-probability vectors, and will never reach the other one.