Definition:Gibbs Sampler

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Definition

The Gibbs sampler is a Markov chain Monte Carlo technique used to give numerical approximations to Bayesian posterior distributions involving $2$ or more variables.

An initial set of values is specified, and new values of each variable are successively simulated from their conditional distributions, given the current values of all other variables.

If the new value is more in accord with the specified distribution, it replaces the current value, otherwise the current value is kept.

The process is continued until an equilibrium is reached.

Also see

• Results about the Gibbs sampler can be found here.

Source of Name

This entry was named for Josiah Willard Gibbs.

Historical Note

The Gibbs Sampler was devised by the brothers Stuart Alan Geman and Donald Jay Geman in $1984$.

It was named after Josiah Willard Gibbs, who was a pioneer of statistical mechanics.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Gibbs sampler