The Gibbs Sampler

Abstract

The previous chapter developed simulation techniques that could be called “generic,” since they require only a limited amount of information about the distribution to be simulated. For example, the generic algorithm ARMS (§6.3.3) aims at reproducing the density f of this distribution in an automatic manner. However, Metropolis-Hastings algorithms can achieve higher levels of efficiency when they take into account the specifics of the target distribution f, in particular through the calibration of the acceptance rate (see §6.4.1). Moving even further in this direction, the properties and performance of the Gibbs sampling method presented in this chapter are very closely tied to the distribution f. This is because the choice of instrumental distribution is essentially reduced to a choice between a finite number of possibilities.

In this place he was found by Gibbs, who had been sent for him in some haste. He got to his feet with promptitude, for he knew no small matter would have brought Gibbs in such a place at all.

G.K. Chesterton, The Innocence of Father Brown