Following standard parametric Bayes applications, there was a
growing need for nonparametric Bayes analysis which seemed to
pose some difficulties. These difficulties were removed by the
the first definitions of Dirichlet processes by Ferguson,
Blackwell and MacQueen. Dirichlet processes became famous after
some easy applications in standard nonparametric Bayes
problems. However, the proofs looked complicated and
mystifying. In spite of this many salient properties of Dirichlet
processes were being established.
The Sethuraman constructive definition of a Dirichlet process
simplified proving such properties and establishing further
properties. Computational Bayes analysis took off in parametric
problems, thanks to MCMC. The importance of the constructive
definition for computational nonparametric Bayes analysis was
recognized immediately and it opened the flood gates for a
multitude of diverse applications.
This talk will traverse through some of these developments.