  The study of properties of mean functionals of random probability measures is
an important area of research in the theory of Bayesian nonparametric
statistics. Many results are now known for random Dirichlet means, but little
is known, especially in terms of posterior distributions, for classes of priors
beyond the Dirichlet process. In this paper, we consider normalized random
measures with independent increments (NRMI's) and mixtures of NRMI. In both
cases, we are able to provide exact expressions for the posterior distribution
of their means. These general results are then specialized, leading to
distributional results for means of two important particular cases of NRMI's
and also of the two-parameter Poisson--Dirichlet process.
