This article presents new operational convergence criteria for the Gib
bs sampler (GS) and related procedures that are useful for determining
whether they not only have converged but also have converged to provi
de reliable results. Three GS convergence criteria are presented and a
pplied: the difference convergence criterion (DC2), the ratio converge
nce criterion (RC(2)), and the anchored ratio convergence criterion (A
RC(2)). Their uses and properties are discussed and examples are analy
zed to illustrate their application.