  By developing data augmentation methods unique to the negative binomial (NB)
distribution, we unite seemingly disjoint count and mixture models under the NB
process framework. We develop fundamental properties of the models and derive
efficient Gibbs sampling inference. We show that the gamma-NB process can be
reduced to the hierarchical Dirichlet process with normalization, highlighting
its unique theoretical, structural and computational advantages. A variety of
NB processes with distinct sharing mechanisms are constructed and applied to
topic modeling, with connections to existing algorithms, showing the importance
of inferring both the NB dispersion and probability parameters.
