A fifty-year retrospective on Ferguson's (1973) Dirichlet process (DP), the prior that first satisfied the two conflicting desiderata for Bayesian nonparametrics — large support and analytical tractability. The authors review three complementary constructions of the DP, all traceable to Ferguson: through finite-dimensional distributions, via normalization of a gamma process, and through predictive distributions. Each perspective deepens understanding and provides a template for generalization — to normalized random measures with independent increments, Gibbs-type priors, and beyond — and the paper argues the process should be called the Ferguson-Dirichlet process.
"Ferguson's 1973 introduction of the Dirichlet process marked a breakthrough in Bayesian nonparametric statistics. For the first time, a prior on the space of probability measures fulfilled two key desiderata: large support and analytical tractability."
A useful synthesis for anyone who knows the DP only through stick-breaking and the CRP: it lays out that those are two of three equivalent doors into the same object, the third — normalizing a gamma random measure — being the one that generalizes most productively (NRMI, normalized inverse-Gaussian, Gibbs-type priors, Pitman-Yor). That completely-random-measure viewpoint is exactly what the wiki's DP-mixture page under-weighted relative to the constructive (Sethuraman) and predictive (Antoniak) routes, so it fills a real gap and points to where modern Bayesian nonparametrics went after the DP. The "Ferguson-Dirichlet process" renaming is a fair tribute; whether it sticks is another matter.