Some Useful Properties of the Dirichlet Process

The aim of this chapter is firstly to recall the close connection between the Dirichlet process and the Gamma process in very general spaces and to show how it can be used to derive interesting properties of the Dirichlet process. Secondly, it is shown that the characterization of the Dirichlet process through independence relations between associated \(\sigma \) -fields entails a nice description of the posterior distribution of the Dirichlet process at points where there is either no or at least one observation.