  This paper presents theory for Normalized Random Measures (NRMs), Normalized
Generalized Gammas (NGGs), a particular kind of NRM, and Dependent Hierarchical
NRMs which allow networks of dependent NRMs to be analysed. These have been
used, for instance, for time-dependent topic modelling. In this paper, we first
introduce some mathematical background of completely random measures (CRMs) and
their construction from Poisson processes, and then introduce NRMs and NGGs.
Slice sampling is also introduced for posterior inference. The dependency
operators in Poisson processes and for the corresponding CRMs and NRMs is then
introduced and Posterior inference for the NGG presented. Finally, we give
dependency and composition results when applying these operators to NRMs so
they can be used in a network with hierarchical and dependent relations.
