This book focuses on the properties associated with the Dirichlet
process, describing its use a priori for nonparametric inference and
the Bayes estimate to obtain limits for the estimable parameter. It
presents the limits and the well-known U- and V-statistics as a
convex combination of U-statistics, and by investigating this convex
combination, it demonstrates these three statistics. Next, the book
notes that the Dirichlet process gives the discrete distribution with
probability one, even if the parameter of the process is continuous.
Therefore, there are duplications among the sample from the
distribution, which are discussed. Because sampling from the Dirichlet
process is described sequentially, it can be described equivalently by
the Chinese restaurant process. Using this process, the
Donnelly-Tavaré-Griffiths formulas I and II are obtained, both of which
give the Ewens' sampling formula. The book then shows the convergence
and approximation of the distribution for its number of distinct
components. Lastly, it explains the interesting properties of the
Griffiths-Engen-McCloskey distribution, which is related to the
Dirichlet process and the Ewens' sampling formula.